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

taangerine | Student

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.


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. 




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.


Combine like terms.


Divide 7 on both sides to isolate the y. 


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




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



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