{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-01-28T03:08:11+00:00","modifiedTime":"2017-01-28T03:08:11+00:00","timestamp":"2022-09-14T18:17:09+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"SAT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33794"},"slug":"sat","categoryId":33794}],"title":"SAT Practice Questions: Graphing Systems of Inequalities","strippedTitle":"sat practice questions: graphing systems of inequalities","slug":"sat-practice-questions-graphing-systems-inequalities","canonicalUrl":"","seo":{"metaDescription":"The SAT Math exam may ask you to graph a system of inequalities. You solve these in the same way as you would for a system of equations: by graphing each inequa","noIndex":0,"noFollow":0},"content":"The SAT Math exam may ask you to graph a system of inequalities. You solve these in the same way as you would for a system of equations: by graphing each inequality and looking for where the shaded regions intersect.\r\n\r\nThe following practice questions ask you to find the areas of intersection on the <em>xy</em>-plane, and then to identify which quadrants will contain them.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li><strong>If the system of inequalities <em>y</em> > <em>x</em> + 3 and <em>y </em>> –<em>x</em> + 2 is graphed in the <em>xy</em>-plane shown here, which quadrants contain all the solutions to the system?\r\n</strong><a href=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\"><img class=\"alignnone size-full wp-image-232770\" src=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\" alt=\"sat1001-quadrants\" width=\"233\" height=\"249\" /></a>\r\n<strong>A. </strong>Quadrants I and II\r\n<strong>B.</strong> Quadrants II and III\r\n<strong>C.</strong> Quadrants III and IV\r\n<strong>D.</strong> Quadrants I and IV</li>\r\n\t<li><strong>If the system of inequalities <em>y</em> > <em>x</em> – 5 and y < 2x – 3 is graphed in the <em>xy</em>-plane shown here, which quadrants contain all the solutions to the system?\r\n<a href=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\"><img class=\"alignnone size-full wp-image-232770\" src=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\" alt=\"sat1001-quadrants\" width=\"233\" height=\"249\" /></a>\r\nA. </strong>Quadrants I, II, and III\r\n<strong>B. </strong>Quadrants II, III, and IV\r\n<strong>C.</strong> Quadrants I, II, and IV\r\n<strong>D.</strong> Quadrants I, III, and IV</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li><strong>The correct answer is Choice (A).</strong>\r\nTo graph <em>y</em> > <em>x</em> + 3, draw a line going upward and crossing the <em>y</em>-axis at 3; the inequality includes all the solutions above that line. To graph <em>y</em> > –<em>x</em> + 2, draw a line going downward and crossing the <em>y</em>-axis at 2; the inequality includes all the solutions above that line. The result is that all the solutions are contained within a <em>V</em> shape with the vertex at right about (0, 3). This <em>V</em> extends upward into Quadrants I and II.</li>\r\n\t<li><strong>The correct answer is Choice (B).</strong>\r\nTo graph <em>y</em> > <em>x</em> – 5, draw a line going upward and crossing the <em>y</em>-axis at –5; the inequality includes all the solutions above that line. To graph <em>y</em> < –2<em>x</em> – 3, draw a line going downward and crossing the <em>y</em>-axis at –3; the inequality includes all the solutions below that line. The result is that all the solutions are contained within a <em>V</em> shape pointing left, with the vertex slightly right of (0, –4). This vertex is contained within Quadrant IV, and the <em>V</em> extends leftward into Quadrants II and III.</li>\r\n</ol>","description":"The SAT Math exam may ask you to graph a system of inequalities. You solve these in the same way as you would for a system of equations: by graphing each inequality and looking for where the shaded regions intersect.\r\n\r\nThe following practice questions ask you to find the areas of intersection on the <em>xy</em>-plane, and then to identify which quadrants will contain them.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li><strong>If the system of inequalities <em>y</em> > <em>x</em> + 3 and <em>y </em>> –<em>x</em> + 2 is graphed in the <em>xy</em>-plane shown here, which quadrants contain all the solutions to the system?\r\n</strong><a href=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\"><img class=\"alignnone size-full wp-image-232770\" src=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\" alt=\"sat1001-quadrants\" width=\"233\" height=\"249\" /></a>\r\n<strong>A. </strong>Quadrants I and II\r\n<strong>B.</strong> Quadrants II and III\r\n<strong>C.</strong> Quadrants III and IV\r\n<strong>D.</strong> Quadrants I and IV</li>\r\n\t<li><strong>If the system of inequalities <em>y</em> > <em>x</em> – 5 and y < 2x – 3 is graphed in the <em>xy</em>-plane shown here, which quadrants contain all the solutions to the system?\r\n<a href=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\"><img class=\"alignnone size-full wp-image-232770\" src=\"https://www.dummies.com/wp-content/uploads/9781119215844-fg0403.gif\" alt=\"sat1001-quadrants\" width=\"233\" height=\"249\" /></a>\r\nA. </strong>Quadrants I, II, and III\r\n<strong>B. </strong>Quadrants II, III, and IV\r\n<strong>C.</strong> Quadrants I, II, and IV\r\n<strong>D.</strong> Quadrants I, III, and IV</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li><strong>The correct answer is Choice (A).</strong>\r\nTo graph <em>y</em> > <em>x</em> + 3, draw a line going upward and crossing the <em>y</em>-axis at 3; the inequality includes all the solutions above that line. To graph <em>y</em> > –<em>x</em> + 2, draw a line going downward and crossing the <em>y</em>-axis at 2; the inequality includes all the solutions above that line. The result is that all the solutions are contained within a <em>V</em> shape with the vertex at right about (0, 3). This <em>V</em> extends upward into Quadrants I and II.</li>\r\n\t<li><strong>The correct answer is Choice (B).</strong>\r\nTo graph <em>y</em> > <em>x</em> – 5, draw a line going upward and crossing the <em>y</em>-axis at –5; the inequality includes all the solutions above that line. To graph <em>y</em> < –2<em>x</em> – 3, draw a line going downward and crossing the <em>y</em>-axis at –3; the inequality includes all the solutions below that line. The result is that all the solutions are contained within a <em>V</em> shape pointing left, with the vertex slightly right of (0, –4). This vertex is contained within Quadrant IV, and the <em>V</em> extends leftward into Quadrants II and III.</li>\r\n</ol>","blurb":"","authors":[{"authorId":8978,"name":"Ron Woldoff","slug":"ron-woldoff","description":" <p><b>Ron Woldoff is founder of National Test Prep, where he helps students succeed on the GMAT, GRE, SAT, ACT, and PSAT. He’s the author of numerous Dummies test prep titles, including <i>GRE 2022 For Dummies</i> and <i>SAT: 1,001 Practice Questions For Dummies.</i></p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8978"}}],"primaryCategoryTaxonomy":{"categoryId":33794,"title":"SAT","slug":"sat","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33794"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":232868,"title":"SAT Writing Practice Problems: Parallel Structure, Agreement, and Tense","slug":"sat-writing-practice-problems-parallel-structure-agreement-tense","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232868"}},{"articleId":232865,"title":"SAT Writing Practice Problems: Logic and Organization","slug":"sat-writing-practice-problems-logic-organization","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232865"}},{"articleId":232862,"title":"SAT Writing Practice Problems: Vocabulary in Context","slug":"sat-writing-practice-problems-vocabulary-context","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232862"}},{"articleId":232859,"title":"SAT Writing Practice Problems: Grammar and Punctuation","slug":"sat-writing-practice-problems-grammar-punctuation","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232859"}},{"articleId":232855,"title":"SAT Reading Practice Problems: Interpreting Visual Elements","slug":"sat-reading-practice-problems-interpreting-visual-elements","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/232855"}}],"fromCategory":[{"articleId":293029,"title":"SAT Prep 2023 For Dummies Cheat Sheet","slug":"sat-prep-2023-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/293029"}},{"articleId":277844,"title":"10 Ways to Get the Most from the Practice SATs","slug":"10-ways-to-get-the-most-from-the-practice-sats","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277844"}},{"articleId":277839,"title":"10 Mistakes You Won’t Make on the SAT","slug":"10-mistakes-you-wont-make-on-the-sat","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277839"}},{"articleId":277836,"title":"Strategies for the SAT Reading Test","slug":"strategies-for-the-sat-reading-test","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277836"}},{"articleId":277833,"title":"Simple Strategies for Taking the SAT Writing and Language Test","slug":"simple-strategies-for-taking-the-sat-writing-and-language-test","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/277833"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282560,"slug":"sat-1001-practice-questions-for-dummies","isbn":"9781119215844","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"amazon":{"default":"https://www.amazon.com/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119215846-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119215846/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/sat-1001-practice-questions-for-dummies-cover-9781119215844-202x255.jpg","width":202,"height":255},"title":"SAT","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p>Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including <i>GRE For Dummies</i> and <i>1,001 GRE Practice Questions For Dummies</i>.</p>","authors":[{"authorId":8978,"name":"Ron Woldoff","slug":"ron-woldoff","description":" <p><b>Ron Woldoff is founder of National Test Prep, where he helps students succeed on the GMAT, GRE, SAT, ACT, and PSAT. He’s the author of numerous Dummies test prep titles, including <i>GRE 2022 For Dummies</i> and <i>SAT: 1,001 Practice Questions For Dummies.</i></p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8978"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","sat"]},{"key":"isbn","values":["9781119215844"]}]\" id=\"du-slot-63221aa5f207a\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","sat"]},{"key":"isbn","values":["9781119215844"]}]\" id=\"du-slot-63221aa5f25f5\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":null,"lifeExpectancySetFrom":null,"dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":232769},"articleLoadedStatus":"success"},"listState":{"list":{},"objectTitle":"","status":"initial","pageType":null,"objectId":null,"page":1,"sortField":"time","sortOrder":1,"categoriesIds":[],"articleTypes":[],"filterData":{},"filterDataLoadedStatus":"initial","pageSize":10},"adsState":{"pageScripts":{"headers":{"timestamp":"2024-03-04T05:50:01+00:00"},"adsId":0,"data":{"scripts":[{"pages":["all"],"location":"header","script":"\r\n<script src=\"https://cdn.optimizely.com/js/10563184655.js\"></script>","enabled":false},{"pages":["all"],"location":"header","script":"\r\n<script>var _comscore = _comscore || [];_comscore.push({ c1: \"2\", c2: \"15097263\" });(function() {var s = document.createElement(\"script\"), el = document.getElementsByTagName(\"script\")[0]; s.async = true;s.src = (document.location.protocol == \"https:\" ? \"https://sb\" : \"http://b\") + \".scorecardresearch.com/beacon.js\";el.parentNode.insertBefore(s, el);})();</script><noscript><img src=\"https://sb.scorecardresearch.com/p?c1=2&c2=15097263&cv=2.0&cj=1\" /></noscript>\r\n","enabled":true},{"pages":["all"],"location":"footer","script":"\r\n<script type='text/javascript'>\r\n(function(){var g=function(e,h,f,g){\r\nthis.get=function(a){for(var a=a+\"=\",c=document.cookie.split(\";\"),b=0,e=c.length;b<e;b++){for(var d=c[b];\" \"==d.charAt(0);)d=d.substring(1,d.length);if(0==d.indexOf(a))return d.substring(a.length,d.length)}return null};\r\nthis.set=function(a,c){var b=\"\",b=new Date;b.setTime(b.getTime()+6048E5);b=\"; expires=\"+b.toGMTString();document.cookie=a+\"=\"+c+b+\"; path=/; \"};\r\nthis.check=function(){var a=this.get(f);if(a)a=a.split(\":\");else if(100!=e)\"v\"==h&&(e=Math.random()>=e/100?0:100),a=[h,e,0],this.set(f,a.join(\":\"));else return!0;var c=a[1];if(100==c)return!0;switch(a[0]){case \"v\":return!1;case \"r\":return c=a[2]%Math.floor(100/c),a[2]++,this.set(f,a.join(\":\")),!c}return!0};\r\nthis.go=function(){if(this.check()){var a=document.createElement(\"script\");a.type=\"text/javascript\";a.src=g;document.body&&document.body.appendChild(a)}};\r\nthis.start=function(){var t=this;\"complete\"!==document.readyState?window.addEventListener?window.addEventListener(\"load\",function(){t.go()},!1):window.attachEvent&&window.attachEvent(\"onload\",function(){t.go()}):t.go()};};\r\ntry{(new g(100,\"r\",\"QSI_S_ZN_5o5yqpvMVjgDOuN\",\"https://zn5o5yqpvmvjgdoun-wiley.siteintercept.qualtrics.com/SIE/?Q_ZID=ZN_5o5yqpvMVjgDOuN\")).start()}catch(i){}})();\r\n</script><div id='ZN_5o5yqpvMVjgDOuN'></div>\r\n","enabled":false},{"pages":["all"],"location":"header","script":"\r\n<script>\r\n (function(h,o,t,j,a,r){\r\n h.hj=h.hj||function(){(h.hj.q=h.hj.q||[]).push(arguments)};\r\n h._hjSettings={hjid:257151,hjsv:6};\r\n a=o.getElementsByTagName('head')[0];\r\n r=o.createElement('script');r.async=1;\r\n r.src=t+h._hjSettings.hjid+j+h._hjSettings.hjsv;\r\n a.appendChild(r);\r\n })(window,document,'https://static.hotjar.com/c/hotjar-','.js?sv=');\r\n</script>","enabled":false},{"pages":["article"],"location":"header","script":" <script src=\"//get.s-onetag.com/bffe21a1-6bb8-4928-9449-7beadb468dae/tag.min.js\" async defer></script>","enabled":true},{"pages":["homepage"],"location":"header","script":"<meta name=\"facebook-domain-verification\" content=\"irk8y0irxf718trg3uwwuexg6xpva0\" />","enabled":true},{"pages":["homepage","article","category","search"],"location":"footer","script":"\r\n<noscript>\r\n<img height=\"1\" width=\"1\" src=\"https://www.facebook.com/tr?id=256338321977984&ev=PageView&noscript=1\"/>\r\n</noscript>\r\n","enabled":true}]}},"pageScriptsLoadedStatus":"success"},"navigationState":{"navigationCollections":[{"collectionId":287568,"title":"BYOB (Be Your Own Boss)","hasSubCategories":false,"url":"/collection/for-the-entry-level-entrepreneur-287568"},{"collectionId":293237,"title":"Be a Rad Dad","hasSubCategories":false,"url":"/collection/be-the-best-dad-293237"},{"collectionId":295890,"title":"Career Shifting","hasSubCategories":false,"url":"/collection/career-shifting-295890"},{"collectionId":294090,"title":"Contemplating the Cosmos","hasSubCategories":false,"url":"/collection/theres-something-about-space-294090"},{"collectionId":287563,"title":"For Those Seeking Peace of Mind","hasSubCategories":false,"url":"/collection/for-those-seeking-peace-of-mind-287563"},{"collectionId":287570,"title":"For the Aspiring Aficionado","hasSubCategories":false,"url":"/collection/for-the-bougielicious-287570"},{"collectionId":291903,"title":"For the Budding Cannabis Enthusiast","hasSubCategories":false,"url":"/collection/for-the-budding-cannabis-enthusiast-291903"},{"collectionId":299891,"title":"For the College Bound","hasSubCategories":false,"url":"/collection/for-the-college-bound-299891"},{"collectionId":291934,"title":"For the Exam-Season Crammer","hasSubCategories":false,"url":"/collection/for-the-exam-season-crammer-291934"},{"collectionId":301547,"title":"For the Game Day Prepper","hasSubCategories":false,"url":"/collection/big-game-day-prep-made-easy-301547"}],"navigationCollectionsLoadedStatus":"success","navigationCategories":{"books":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/books/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/books/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/books/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/books/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/books/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/books/level-0-category-0"}},"articles":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/articles/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/articles/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/articles/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/articles/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/articles/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/articles/level-0-category-0"}}},"navigationCategoriesLoadedStatus":"success"},"searchState":{"searchList":[],"searchStatus":"initial","relatedArticlesList":[],"relatedArticlesStatus":"initial"},"routeState":{"name":"Article3","path":"/article/academics-the-arts/study-skills-test-prep/sat/sat-practice-questions-graphing-systems-inequalities-232769/","hash":"","query":{},"params":{"category1":"academics-the-arts","category2":"study-skills-test-prep","category3":"sat","article":"sat-practice-questions-graphing-systems-inequalities-232769"},"fullPath":"/article/academics-the-arts/study-skills-test-prep/sat/sat-practice-questions-graphing-systems-inequalities-232769/","meta":{"routeType":"article","breadcrumbInfo":{"suffix":"Articles","baseRoute":"/category/articles"},"prerenderWithAsyncData":true},"from":{"name":null,"path":"/","hash":"","query":{},"params":{},"fullPath":"/","meta":{}}},"dropsState":{"submitEmailResponse":false,"status":"initial"},"profileState":{"auth":{},"userOptions":{},"status":"success"}}

SAT Practice Questions: Graphing Systems of Inequalities

By: Ron Woldoff and

Updated: 01-28-2017

From The Book: SAT

SAT

Book image

Explore Book Buy On Amazon

The SAT Math exam may ask you to graph a system of inequalities. You solve these in the same way as you would for a system of equations: by graphing each inequality and looking for where the shaded regions intersect.

The following practice questions ask you to find the areas of intersection on the xy-plane, and then to identify which quadrants will contain them.

Practice questions

If the system of inequalities y > x + 3 and y > –x + 2 is graphed in the xy-plane shown here, which quadrants contain all the solutions to the system?
A. Quadrants I and II B. Quadrants II and III C. Quadrants III and IV D. Quadrants I and IV
If the system of inequalities y > x – 5 and y < 2x – 3 is graphed in the xy-plane shown here, which quadrants contain all the solutions to the system?
A. Quadrants I, II, and III B. Quadrants II, III, and IV C. Quadrants I, II, and IV D. Quadrants I, III, and IV

Answers and explanations

The correct answer is Choice (A). To graph y > x + 3, draw a line going upward and crossing the y-axis at 3; the inequality includes all the solutions above that line. To graph y > –x + 2, draw a line going downward and crossing the y-axis at 2; the inequality includes all the solutions above that line. The result is that all the solutions are contained within a V shape with the vertex at right about (0, 3). This V extends upward into Quadrants I and II.
The correct answer is Choice (B). To graph y > x – 5, draw a line going upward and crossing the y-axis at –5; the inequality includes all the solutions above that line. To graph y < –2x – 3, draw a line going downward and crossing the y-axis at –3; the inequality includes all the solutions below that line. The result is that all the solutions are contained within a V shape pointing left, with the vertex slightly right of (0, –4). This vertex is contained within Quadrant IV, and the V extends leftward into Quadrants II and III.

About This Article

This article is from the book:

SAT ,

About the book author:

Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including GRE For Dummies and 1,001 GRE Practice Questions For Dummies.

This article can be found in the category:

SAT ,