3-2 Solving Systems Algebraically (p. 125)

Algebra 2

Prentice Hall, 2007

Content Objectives

You will…

Solve a system of linear equations using the process of SUBSTITUTION.

Solve a system of linear equations using the process of ELIMINATION.

Be able to decide which method would be the easiest to use.

Substitution Method

1. Choose 1 equation and solve for the “easiest” variable.

2. Substitute that “expression” into the other equation for the variable it represents.

3. Solve for the 2nd variable.

4. Substitute the value of that variable into 1 of the 2 original equations to find the value of the 1st variable.

Example

Solve the system using substitution:

Hint: Solve for y in the 1st equation.€

3x − y = 0

4x + 3y = 26

Example

Solve the system using substitution:

Hint: Solve for x in either equation.€

x −2y = −1

x + 4y = 6

Elimination Method

1. Write both equations in Standard Form.2. “Doctor-up” 1 or both equations so that the

x’s OR y’s are zero pairs.3. Combine the 2 equations, thereby

eliminating one of the variables.4. Solve for the remaining variable.5. Substitute the value of that variable into

either of the original equations to find the other variable.

Example

Solve the system using elimination:

Hint: Doctor-up one equation in order to eliminate x.€

x −2y = −1

x + 4y = 6

Example

Solve the system using elimination:

Hint: Doctor-up both equations in order to eliminate x OR y... Your choice!€

3x + 7y =15

5x + 2y = −4

Example

Solve the system using whichever method you want:

No Solution!

€

−2x + 4y = 6−3x + 6y = 8

What if…?

… both variables get eliminated and you end up with a false statement?

NO Solution

… both variables get eliminated and you end up with a true statement?

Infinite # of Solutions

Homework

3-2 p. 128: m.o.5 (5-50)