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

Textbook Question

Chapter 3, 3.2 - Problem 4 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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taangerine | Student, Grade 12 | (Level 1) Valedictorian

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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

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