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

1. Pick an equation to rearrange
2. Substitute equation
3. Solve equation
4. Substitute the number just found, back into the rearranged equation
5. 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