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.