SOLUTION: Solve using Substitution method 2x+3y=-3 2x-y=6

Question 888789: Solve using Substitution method
2x+3y=-3
2x-y=6
Found 2 solutions by Alan3354, algebrapro18:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve using Substitution method
2x+3y=-3
2x-y=6 --> y = 2x - 6
sub for y in the 1st eqn

Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Steps for solving systems using the Substitution method:
1)Solve one of the equations for either x or y
2)Plug that expression into the other equation and solve for either x or y(which ever one you didn't solve for in step 1)
3)Plug your solution from 2 into the expression in step 1 and solve for the varable.

I know this is about as clear as mud but I'm hoping it will help you keep things straight in the future. That is the process you will ALWAYS follow regardless of the problem.

So for our problem we:
1) Solve the second equation for y. I chose the second equation and y because y has no coefficient by it in the second equation(well except -1 but that doesn't matter).

2x-y=6 Subtract 2x from both sides to get -y by its self
-y = -2x+6* Divide both sides by -1 to get y by its self
y = 2x-6

*Remember 6-2x is 6-2x because you can not combine unlike terms. 6 is just 6 and 2 is being multiplied by x which makes them unlike.

2)Plug in into the first equation and solve for x.

2x+3y=-3 Plug 2x-6 in for y.
2x+3(2x-6)=-3 Distribute
2x+6x-18=-3 Combine like terms
8x-18=-3 add 18 to both sides
8x = 15 divide both sides by 8
x= 15/8

3) Plug x=15/8 into y=2x-6 and solve for y.

y=2x-6 plug 15/8 in for x
y=2(15/8)-6 Multiply 2*15/8
y=15/4-6 Get a common denominator
y=(15-24)/4 Subtract
y=-9/4
So your final solution is (15/8,-9/4).
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