solve this system of equations using the linear combination method

-3x+12y=-27
5x+20y=15

commonly called the elimination method

I would multiply the first by 5
---> -15x + 60y = - 135
multiply the 2nd by 3
---> 15x + 60y = 45
add them:
120y = - 90
y = -90/120 = -3/4

sub that into either of the two originals to get the x

To solve the system of equations using the linear combination method, follow these steps:

Step 1: Multiply one or both equations by a constant so that the coefficient of one variable will be the same in both equations.

Let's multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations equal:

-3x + 12y = -27 --> 5(-3x + 12y) = 5(-27) --> -15x + 60y = -135
5x + 20y = 15 --> 3(5x + 20y) = 3(15) --> 15x + 60y = 45

Step 2: Add or subtract the modified equations to eliminate one variable. In this case, we'll eliminate the x variable.

(-15x + 60y) + (15x + 60y) = -135 + 45
Combine like terms:
0x + 120y = -90
120y = -90
Divide both sides by 120:
y = -90/120
y = -3/4

Step 3: Substitute the value of y back into one of the original equations to solve for x.

Let's use the first equation:
-3x + 12(-3/4) = -27
-3x - 9 = -27
-3x = -27 + 9
-3x = -18
Divide both sides by -3:
x = -18/-3
x = 6

So the solution to the system of equations is x = 6, y = -3/4.