SAT Math Multiple Choice Question 377: Answer and Explanation
If (a, b) represents the solution to the system of equations shown in the graph and a = -3b, then which of the following could be the value of a + b?
- A. -9
- B. 0
- C. 3
- D. 6
Correct Answer: A
Category: Heart of Algebra / Systems of Linear Equations
Strategic Advice: Graphically, the solution to a system of equations is the point or points where the graphs intersect. Whenever a graph with no grid-lines or axis labels is shown, you are usually interested primarily in the sign of the coordinates of a point, not the actual values.
Getting to the Answer: The graphs intersect in Quadrant 2 of the coordinate plane, so the x-value of the point of intersection (or a) is negative, and the y-value (or b) is positive. The question states that a = –3b, so you can eliminate B right away—the coordinates would have to be equal if their sum was 0. Now try Picking Numbers. Let b = 1, which means a = –3 and the sum of a + b is –2, which is not one of the answer choices. Try another pair: If b = 2, then a = –6, and the sum is –4. This is still not one of the answer choices, but you should see a pattern—the x-coordinate will always overpower the y-coordinate, resulting in a negative sum, so the correct answer must be (A).