SAT Math Multiple Choice Question 630: Answer and Explanation
15. x - 3y = -2
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
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
Multiply by x and simplify:
x2 - 15 = -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.