Solve this system of equations using elimination (Show your work).
3x+6y=18
3x+y=-7
Show work
1. Multiply the second equation by 6 to make the coefficients of x in both equations cancel when added together:
6(3x + y) = 6(-7)
18x + 6y = -42
2. Now we have:
3x + 6y = 18
18x + 6y = -42
3. Subtract the first equation from the second equation to eliminate y:
18x + 6y - (3x + 6y) = -42 - 18
15x = -60
x = -4
4. Substitute x = -4 back into one of the original equations to solve for y. Let's use the first equation:
3(-4) + 6y = 18
-12 + 6y = 18
6y = 30
y = 5
Therefore, the solution to the system of equations is x = -4 and y = 5.