# SAT Practice Questions: Graphing Systems of Inequalities

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**Quadrants I, II, and III*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.

**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*< –2*x*– 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.