Question

Solve the system by elimination. {2×+6y=-12; 5×-5y=10

Answer 1

To solve the system using elimination, we aim to eliminate one of the variables by adding or subtracting the two equations.

First, let's multiply the second equation by 2 to make the coefficients of x in both equations the same:

2(5x - 5y) = 2(10)
10x - 10y = 20

Now, we have the two equations:

2x + 6y = -12
10x - 10y = 20

Next, we will eliminate the y variable.

Multiply the first equation by -5 and the second equation by 1:

-5(2x + 6y) = -5(-12)
10x + 30y = 60

1(10x - 10y) = 1(20)
10x - 10y = 20

Now, we have the two equations:

10x + 30y = 60
10x - 10y = 20

By subtracting the second equation from the first equation, the x variable will be eliminated:

(10x + 30y) - (10x - 10y) = 60 - 20
10x + 30y - 10x + 10y = 40
40y = 40
y = 1

Substitute the value of y back into either of the original equations, such as the first equation:

2x + 6(1) = -12
2x + 6 = -12
2x = -12 - 6
2x = -18
x = -9

The solution to the system of equations is x = -9 and y = 1.