Question

Solve the system by substitution. 6x + 3y = -6 2x + y = -2

Answer 1

Solutions 

First Lets solve for this equation $6x + 3y = -6$ 

$6x + 3y = -6$ 

$6x+3(-2-2x)=-6$ 

$-6=-6$ 

Therefore this given equation is a dependent system. 

Solve for $2x + y = -2$ 

$2x+y=-2$ 

$y=-2-2x$ 

There are too many solutions to these equations. 

Answer 2

6x + 3y = -6
2x + y = -2

Solve both equations for the same variable, in this case, I'll solve for y.

2x + y = -2   Subtract 2x from both sides
y = -2x -2

6x + 3y = -6         Subtract 6x from both sides
        3y = -6x -6   Divide both sides by 3
          y = -2x -2  

Once you have them solved you can set them equal to each other and solve.

-2x -2 = -2x -2 

But, these two equations are the same, so any number you put in for x will work. The answer to the system is infinite solutions.