Final answer:
The solution to the system of equations is x = 1 and y = -9. To solve the system of equations using elimination, multiply the equations by constants to make the coefficients of one variable the same. Subtract the equations to eliminate the variable and solve for the remaining variable.
Step-by-step explanation:
To solve the system of equations using elimination, we need to eliminate one variable by multiplying one or both equations by a constant, such that the coefficients of one variable are the same in both equations. In this case, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of 'x' the same. This gives us:
12x + 4y = -24
12x + 9y = 21
Now we can subtract the first equation from the second equation to eliminate 'x':
12x + 9y - (12x + 4y) = 21 - (-24)
-5y = 45
Dividing both sides by -5, we get:
y = -9
Now we can substitute the value of 'y' back into one of the original equations to find 'x'. Using the first equation:
6x + 2(-9) = -12
6x - 18 = -12
Adding 18 to both sides, we have:
6x = 6
Dividing both sides by 6, we get:
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -9.