# SAT Math Multiple Choice Question 819: Answer and Explanation

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**Question: 819**

**9.**

A system of inequalities and the corresponding graph are shown above. Which part ofthe graph could represent all of the solutions to the system?

- A. A
- B. B
- C. C
- D. D

**Correct Answer:** D

**Explanation:**

**D**

**Difficulty:** Medium

**Category:** Heart of Algebra / Inequalities

**Strategic Advice:** The solution to a system of inequalities is the region of the graph that satisfies both inequalities. Pay careful attention to which line is dashed and which is solid as you analyze the regions of the graph.

**Getting to the Answer:** The solution set for the inequality *y* > *x* is the union of the sections of the graph that are above the dashed line, which are A and D. The solution set for the inequality 3*y* ≤ -4*x* + 6 is the union of the sections that are below the solid line, which are C and D. The solution set for the system of inequalities consists of all the points that satisfy both inequalities, which are contained within region (D).