This week in math 10 I learned how to solve equations with using substitution. The steps for substitute are as fallows:

- Pick an equation to rearrange
- Substitute equation
- Solve equation
- Substitute the number just found, back into the rearranged equation
- Verify solution on both equations

The equations being solved for this example will be y-x=1 and 2x+3y=18.

The first step is to pick an equation to rearrange and rearrange it. The best option is always the equation with a coefficient of 1. So, the best option for rearranging is y-x=1.

y-x=1

y-x+x=1+x

y=1+x

The second step is to insert the rearranged equation and substitute into the second equation. We are going to put y=1+x into 2x+3y=18. We are going to want to put 1+x into the equation where the y is in the second equation because y is equal to 1+x.

y=1+x and 2x+3y=18 becomes 2x+3(1+x)=18

If you notice, the equation has become a simple 9^{th} grade equation.

The next step is to solve the equation

2x+3(1+x)=18

2x+3+3x=18

5x+3=18

5x+3-3=18-3

5x=15

5x/5=15/5

x=3

Now to take the number we found (3) and insert it back into the rearranged equation (y=1+x).

y=1+4

y=4

Now to verify the numbers in both equation

y-x=1

4-3=1

2x+3y=18

2(3)+3(4)=18

6+12=18