SAT Math Multiple Choice Question 630: Answer and Explanation

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Question: 630

15. x - 3y = -2

Images

The values of x that satisfy the system of equations above also satisfy which of the following equations?

  • A. (x - 5)(x + 3) = 0
  • B. (x - 3)(x + 5) = 0
  • C. (x - 2)(x - 5) = 0
  • D. (x + 2)(x + 5) = 0

Correct Answer: B

Explanation:

B

Advanced Mathematics (linear and nonlinear systems) HARD

First, notice that the question is only asking us to find values of x, so it's a good idea to substitute in order to eliminate y from the system.

x - 3y = -2

Substitute Images:

Images

Multiply by x and simplify:

x2 - 15 = -2x

Add 2x:

x2 + 2x - 15 = 0

Factor using Sum-Product Method:

(x - 3)(x + 5) = 0

Therefore, the values of x that satisfy the original system also satisfy the equation

(x - 3)(x + 5) = 0.

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