# `x + 3y = -2` `-4x - 5y = 8` Solve the system using the substitution method.

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We have the equations: `x+3y=-2` and `-4x-5y=8` . We have to isolate one of the equations' variables in order to do the substitution method. In this case, let's isolate the x in the first equation.

Rewrite the equation.

`x+3y=-2`

Since it is addition next to the x, we have to do the opposite operation to isolate x. Subtract 3y on both sides to isolate x.

`x+3y-3y=-2-3y`

Simplify.

`x=-2-3y`

Now, plug in this equation into the 2nd equation we have to solve.

2nd equation before plug-in: `-4x-5y=8`

2nd equation after plug-in: `-4(-2-3y)-5y=8`

Distribute the -4.

`8+12y-5y=8`

Combine like terms.

`7y=0`

Divide 7 on both sides to isolate the y.

`y=0`

Now that you have found y, find x by plug in the solution of y into any the original equations.

`x+3(0)=-2`

Simplify

`x=-2`

CHECK: plug in the solution of x and y into both equations to see if you got the correct answer.

`-2+3(0)=-2`

`-4(-2)-6(0)=8`

Since we checked the answer, and the answer came out to be -2 and 8 in the first and second equation, respectively... **x=-2, y=0**