Systems of Linear EquationsThe Substitution Method

Previous Lessons0You have already learned the following…0How to solve equation with two variables0Set up and solve a function table0Input vs. output0Ordered pair solution is where the two

linear equation intersect on a coordinate plane

0How to solve using the Elimination Method

“Substitution”0What does it mean to

substitute?

0Definition: In Algebra "Substitution" means putting numbers where the letters are.

Using the Substitution Method

Example 1Equation One x + y = 8Equation Two x + 2y = 10

Step 1: Select one equation. Solve for one variable to be isolated on one side of the equal sign.

x + y = 8subtract y from both sides -y -y

x = 8 - y

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 = 10New equation: (8 – y) + 2y = 10

Combine like Terms (8 – y) + 2y = 10 8 + y = 10

Subtract 8 -8 -8y = 2

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

Final Solution:

( 6, 2 )

Check: Plug both values into one of the original equations.

x + y = 86 + 2 = 8 8 = 8

Copy and Solve

Complete these problems for homework and we will review tomorrow