how do you slove x+3y=-30

9x-12y=3
with substitution and elimation

To solve the system of equations:

1) Substitution Method:
Step 1: Solve one equation for one variable (in terms of the other variable).
From the first equation, solve for x:
x = -3y - 30

Step 2: Substitute the expression for x in the other equation.
Replace x in the second equation with -3y - 30:
9(-3y - 30) - 12y = 3

Step 3: Simplify and solve for y.
-27y - 270 - 12y = 3
-39y - 270 = 3
-39y = 3 + 270
-39y = 273
y = -7

Step 4: Substitute the value of y back into the first equation to find x:
x = -3(-7) - 30
x = 21 - 30
x = -9

So, the solution to the system of equations is x = -9 and y =-7.

2) Elimination Method:
Step 1: Multiply the first equation by the necessary factor to make the coefficients of x in both equations equal.
Multiply the first equation by 3 and the second equation by -1:
3(x + 3y) = 3(-30) (Equation 1)
-1(9x - 12y) = -1(3) (Equation 2)
Simplify:
3x + 9y = -90 (Equation 3)
-9x + 12y = -3 (Equation 4)

Step 2: Add Equation 3 and Equation 4 together to eliminate x:
(3x + 9y) + (-9x + 12y) = -90 + (-3)
-6x + 21y = -93

Step 3: Make one variable the subject of equation by solving one of the equations for that variable. Let's take Equation 3:
3x + 9y = -90
3x = -90 - 9y
x = -30 - 3y

Step 4: Substitute the expression for x in Equation 4 with the expression from Equation 3:
-6(-30 - 3y) + 21y = -93
180 + 18y + 21y = -93
39y = -273
y = -7

Step 5: Substitute the value of y back into the expression for x from Equation 3:
x = -30 - 3(-7)
x = -30 + 21
x = -9

So, the solution to the system of equations is x = -9 and y = -7.