Answers are in bold everything else is the steps needed to get there.

If we are doing substitution we need to find out what one of the variables is equal to and then replace whatever that variable was equal to in the other equation and solve. The nice thing is that in this problem it already tells us that y=5x+1. This means we need to replace the y in the other equation with 5x+1. It should look like this.

2(5x+1)-6x=10

Distribute the 2 by multiplying it by both the 5x and the 1. You should get

10x+2-6x=10

Combine the x's that are like variables

4x+2=10

Subtract the 2 from both sides of the equation to get x alone

4x=8

Divide by 4 on both sides to get x=2.

Now to find y pick either equation and plug in x=2. For the first one it will be.

y=5(2)+1 y=10+1 y=11

Final answer is (2,11)

Just for kicks let's put x=2 into the other equation just to make sure it checks out as 11.

2y-6(2)=10 2y-12=10 2y=22 y=11

Checked out both equations we can be positive that (2,11) is right!

I hope this was helpful. Please let me know if you need any clarification

Sep 11th, 2015

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