Lesson 4-2: Solving Systems – Substitution & Linear

Combinations

Objectives:Students will:Solve systems of equations using substitution and linear combinations

Substitution

1. Substitute what a variable equals in one equation for itself in the other equation.

2. Solve for that variable.

3. Substitute the value of this variable back into one of the original equations

4. Solve for the other variable.

5. Check that the two values solves both equations

Example 1 Solve the system 5x + 3y = 65x + 3y = 6

x – y = -1x – y = -1

Example 2 Solve the system 5x + 3y = 65x + 3y = 6

x – y = -1x – y = -1

Example 3 We want a different method for this one 5x + 3y = 175x + 3y = 17

-5x + 2y = 3-5x + 2y = 3

Linear Combination (ELIMINATION)1. Set up both equations in Standard Form : Ax + By = C

2. Obtain opposite x or y terms. Multiply an equation by a number if you have to get opposites.

3. Add the equations vertically – x’s or y’s will eliminate

4. Solve for the remaining variable.

5. Substitute the value of this variable back into one of the original equations

6. Solve for the other variable.

7. Check that the two values solves both equations

Example 3 Use elimination 5x + 3y = 175x + 3y = 17

-5x + 2y = 3-5x + 2y = 3

Example 46x + 2y = -166x + 2y = -16

-12x - 5y = 31-12x - 5y = 31

Example 5

231

43

132

21

yx

yx

HW 35