**Video** on Solving by Substitution

### The Substitution Method

First, let's review how the substitution property works in general

**Review Example 1**

**Review Example 2**

##### Substitution Example 1

Let's re-examine system pictured up above.

$ \red{y} = 2x + 1 \text{ and } \red{y} = 4x -1 $

Step 1We are going to use substitution like we did in review example 2 above

Now we have 1 equation and 1 unknown, we can solve this problem as the work below shows.

The last step is to again use substitution, in this case we know that x = 1 , but in order to find the y value of the solution, we just substitute **x =1** into either equation.

$$ y = 2x + 1 \\ y = 2\cdot \red{1} + 1 = 2 + 1 =3 \\ \\ \boxed{ \text{ or you use the other equation}} \\ y = 4x -1 \\ y = 4\cdot \red{1}- 1 = 4 - 1 = 3 \\ \text{solution = }( 1,3) $$

You can also solve the system by graphing and see a picture of the solution below: