X-3y=-12 and 4x+6y=-12 substitution

x = -6

y = 2

Step-by-step explanation:

1. Approach

x - 3y = -12

4x + 6y = -12

In this problem, it would likely be easier to use elimination, but since the problem specifically says that one must use substitution, substitution will be used. Substitution is when one solves one of the equations for a variable, similar to solving a literal equation. The one will substitute in the value of the variable into the other equation and solve for the other varibale. Then one will finally back substitute in that value of the other variable to find the value of the first variable, hence solving the equation.

2. Solve equation 1

x - 3y = -12

Solve the literal equation with inverse operations;

x - 3y = -12

   +3y    + 3y

x = 3y - 12

3. Substitute the answer into the second equation

4x + 6y = -12

x = 3y - 12

4 ( 3y - 12 ) + 6y = -12

Distribute;

12y - 48 + 6y = -12

Simplify;

12y - 48 + 6y = -12

18y - 48 = -12

Inverse operations;

18y - 48 = -12

     +48     +48

18y = 36

/18   /18

y = 2

4. Backsolve for x

Substitute the value for y back into the equation for x and solve

x = 3y - 12

y = 2

x = 3(2) - 12

x = 6 - 12

x = -6