# SAT Math Multiple Choice Question 267: Answer and Explanation

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**Question: 267**

**12.**

Which of the following systems of inequalities could be represented by the graph shown?

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

**Correct Answer:** D

**Explanation:**

D

Difficulty: Hard

Category: Heart of Algebra / Inequalities

Strategic Advice: The system in the graph shows shading on opposite sides of two parallel lines, which means there is no solution to the system. This means you're looking for two equations with the same slope, different y-intercepts, and different inequality symbols.

Getting to the Answer: The equations are all given in standard form (Ax + By = C). It would be very time-intensive to convert all four systems to slope-intercept form, so look for ways to eliminate choices more quickly. Each line in the graph falls 1 unit and runs 3 units, so you need to find two lines that have a slope of Use the trick to quickly determine the slopes. The lines in A have a slope of so eliminate A; the lines in B have a slope of so eliminate B; the lines in C have a slope of so eliminate C (pay attention to the sign). This means (D) must be correct. The lines in (D) have a slope of which matches the graph. You don't have to check the shading because none of the other slopes were a match.