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

Answer 1

To solve the system using elimination, we can multiply the first equation by 5 and the second equation by 2 to get the same coefficient for x:

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

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

Now, we can subtract the second equation from the first equation to eliminate the x term:

(10x + 30y) - (10x - 10y) = -60 - 20
10x + 30y - 10x + 10y = -80
40y = -80
y = -80/40
y = -2

Now, substitute the value of y back into one of the original equations:

2x + 6(-2) = -12
2x - 12 = -12
2x = 0
x = 0/2
x = 0

Therefore, the solution to the system is x = 0 and y = -2.