Question

Choose a system of equations with the same solution as the following system: 6x + 2y = −6 3x − 4y = −18

Answer 1

I do know that y = 3 and that x = -2, so any system that has that solution is correct.

Explanation:

Multiplying the second equation by -2 and adding the equations will cancel out the x variable. The remaining equation is:

10y = 30. Therefore, y must be 3. Substituting y in for the first equation, we get:

6x + 6 = -6. That means x must be -2. I checked my work with the second equation:

-6 - 12 = -18.

The system results in a true statement, so the answer is y = 3 and x = -2.

Answer 2

12x+4y=-12

6x-8y=-18

Explanation:

Rewriting them:

1) 6x+2y=-6 → 3x+y=-3 →y=-3-3x

2) 3x-4y=-18 →-4y=-18-3x →y=9/2 -3/4x

By the Addition Method, the Solution is x=-2 and y=3

To have another pair of equations with the same solution, it is enough to multiply both equations, by the same number. This will keep the proportionality between the dependent variables (6x and 2y) and (3x and -4y) and the independent variables (-6 and respectively -18).

So a possible pair of equations with the same solution is (among others)

12x+4y=-12

6x-8y=-18