Question

Identify a possible first step using the elimination method to solve the system and then find the solution to the system. 2x – 3y = 6 3x – y = 2 A) Multiply first equation by 3 and second equation by 2, solution (0, 2). B) Multiply first equation by -3 and second equation by 2, solution (0, 2). C) Multiply first equation by 3 and second equation by 2, solution (-2, 0). D) Multiply first equation by -3 and second equation by 2, solution (0, -2).

Answer 1

The answer is D

2x - 3y =  6  multiply this by -3
3x - y = 2 Multiply this by 2

-6x + 9y = -18
6x  - 2y = 4           Add the 2 equations:-

7y = -14   so y = -2
Substitute y = -2 in second equation:-
3x - (-2) = 2
3x = 2-2 = 0  
x = 0

solution is (0,-2)

Answer 2

Answer:

d

Step-by-step explanation:

The step multiply x by 2 in the first equation and subtract the second equation will NOT produce a system with the same solution. The entire equation must be multiplied by 2.

Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.