1. Systems of Linear Equations The Substitution Method

2. Previous Lessons 0 You have already learned the following… 0 How to solve equation with two variables 0 Set up and solve a function table 0 Input vs. output 0 Ordered pair solution is where the two linear equation intersect on a coordinate plane Elimination Method 0 How to solve using the Elimination Method

3. “Substitution” 0 What does it mean to substitute? 0 Definition: In Algebra "Substitution" means putting numbers where the letters are.

4. Using the Substitution Method

5. Example 1 Equation Onex + y = 8 Equation Two x + 2y = 10 Solve for one variable Step 1: Select one equation. Solve for one variable to be isolated on one side of the equal sign. x + y = 8 subtract y from both sides -y -y x = 8 - y

6. Substitute Step 2: Substitute this expression into the second equation to find the value of the one variable. Equation one: x = 8 – y Equation two: x + 2y = 10 New equation : (8 – y) + 2y = 10 Combine like Terms (8 – y) + 2y = 10 8 + y = 10 Subtract 8 -8 -8 y = 2

7. Substitute Step 3: Substitute this value to find the value of the other variable. y = 2 x + y = 8 x + 2 = 8 Subtract 2 -2 -2 x = 6

8. Final Solution: ( 6, 2 ) Check: Plug both values into one of the original equations. x + y = 8 6 + 2 = 8 8 = 8

11. Copy and Solve Complete these problems for homework and we will review tomorrow