{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-01-28T03:16:53+00:00","modifiedTime":"2017-01-28T03:16:53+00:00","timestamp":"2022-09-14T18:17:10+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: Solving Systems of Equations","strippedTitle":"sat practice questions: solving systems of equations","slug":"sat-practice-questions-solving-systems-equations","canonicalUrl":"","seo":{"metaDescription":"You will probably encounter some questions on the SAT Math exam that deal with systems of equations. In the following practice questions, you're given the syste","noIndex":0,"noFollow":0},"content":"You will probably encounter some questions on the SAT Math exam that deal with systems of equations. In the following practice questions, you're given the system of equations, and you have to find the value of the variables <em>x</em> and <em>y</em>.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li><strong>Based on this system of equations, what is the value of </strong>\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1901.gif\"><img class=\"alignnone size-full wp-image-232775\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1901.gif\" alt=\"SAT1001_eq1901\" width=\"64\" height=\"47\" /></a>\r\n7<em>x</em> + 3<em>y</em> = 4\r\n3<em>x</em> + 2<em>y</em> = 2</li>\r\n\t<li><strong>Based on this system of equations, what is the value of <em>x</em> + <em>y</em>?</strong>\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1902.gif\"><img class=\"alignnone size-full wp-image-232776\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1902.gif\" alt=\"SAT1001_eq1902\" width=\"91\" height=\"99\" /></a></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 1.</strong>\r\nYou don't need separate values of <em>x</em> or <em>y</em>, so don't bother substituting. Simply subtract the equations and divide by 2:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1903.gif\"><img class=\"alignnone size-full wp-image-232777\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1903.gif\" alt=\"SAT1001_eq1903\" width=\"103\" height=\"132\" /></a></li>\r\n\t<li><strong>The correct answer is 6.</strong>\r\nSubtract the equations:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1904.gif\"><img class=\"alignnone size-full wp-image-232778\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1904.gif\" alt=\"SAT1001_eq1904\" width=\"117\" height=\"100\" /></a>\r\nA common denominator works, but you could also multiply everything by 6:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1905.gif\"><img class=\"alignnone size-full wp-image-232779\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1905.gif\" alt=\"SAT1001_eq1905\" width=\"109\" height=\"83\" /></a></li>\r\n</ol>","description":"You will probably encounter some questions on the SAT Math exam that deal with systems of equations. In the following practice questions, you're given the system of equations, and you have to find the value of the variables <em>x</em> and <em>y</em>.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li><strong>Based on this system of equations, what is the value of </strong>\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1901.gif\"><img class=\"alignnone size-full wp-image-232775\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1901.gif\" alt=\"SAT1001_eq1901\" width=\"64\" height=\"47\" /></a>\r\n7<em>x</em> + 3<em>y</em> = 4\r\n3<em>x</em> + 2<em>y</em> = 2</li>\r\n\t<li><strong>Based on this system of equations, what is the value of <em>x</em> + <em>y</em>?</strong>\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1902.gif\"><img class=\"alignnone size-full wp-image-232776\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1902.gif\" alt=\"SAT1001_eq1902\" width=\"91\" height=\"99\" /></a></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 1.</strong>\r\nYou don't need separate values of <em>x</em> or <em>y</em>, so don't bother substituting. Simply subtract the equations and divide by 2:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1903.gif\"><img class=\"alignnone size-full wp-image-232777\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1903.gif\" alt=\"SAT1001_eq1903\" width=\"103\" height=\"132\" /></a></li>\r\n\t<li><strong>The correct answer is 6.</strong>\r\nSubtract the equations:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1904.gif\"><img class=\"alignnone size-full wp-image-232778\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1904.gif\" alt=\"SAT1001_eq1904\" width=\"117\" height=\"100\" /></a>\r\nA common denominator works, but you could also multiply everything by 6:\r\n<a href=\"https://www.dummies.com/wp-content/uploads/SAT1001_1905.gif\"><img class=\"alignnone size-full wp-image-232779\" src=\"https://www.dummies.com/wp-content/uploads/SAT1001_1905.gif\" alt=\"SAT1001_eq1905\" width=\"109\" height=\"83\" /></a></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. 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SAT Practice Questions: Solving Systems of Equations

By: Ron Woldoff and

Updated: 01-28-2017

From The Book: SAT

SAT

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You will probably encounter some questions on the SAT Math exam that deal with systems of equations. In the following practice questions, you're given the system of equations, and you have to find the value of the variables x and y.

Practice questions

Based on this system of equations, what is the value of
7x + 3y = 4 3x + 2y = 2
Based on this system of equations, what is the value of x + y?

Answers and explanations

The correct answer is 1. You don't need separate values of x or y, so don't bother substituting. Simply subtract the equations and divide by 2:
The correct answer is 6. Subtract the equations:
A common denominator works, but you could also multiply everything by 6:

About This Article

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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.

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