Objective:Objective: Solve a system of two linear Solve a system of two linear equations in two variables by equations in two variables by

elimination.elimination.

Standard:Standard: 2.8.11.H. Select and use an 2.8.11.H. Select and use an appropriate strategy to solve appropriate strategy to solve

systems of equations.systems of equations.

3.2 Solving Systems by Elimination

I. Elimination MethodThe elimination method involves multiplying and combining the equations in a system in

order to eliminate a variable.1. Arrange each equation so they are in the same form.

2. Choose to eliminate either x or y.

3. If the coefficients of the variable you chose to eliminate are different, multiply one or both equations to make the coefficients the same size but opposite sign.

4. Add the like terms of the equations

5. Use substitution to solve for the remaining variable.

I. Independent SystemsEx 1. Use elimination to solve the

system. Check your solution.

2x + y = 8 x – y = 10

2x + 5y = 15 –4x + 7y = -13

Ex 2. Use elimination to solve the system. Check your solution.

4x – 3y = 15 8x + 2y = -10

Use elimination to solve the system. Check your solution.

Ex 2. This table gives production costs and selling

prices per frame for two sizes of picture frames.How many of each size should be made andsold if the production budget is $930 and the

expected revenue is $1920?

SmallSmall LargeLarge TotalTotalProductionProduction

CostCost$5.50$5.50 $7.50$7.50 $930$930

Selling Selling PricePrice

$12$12 $15$15 $1920$1920

5.5x + 7.5y = 93012x + 15y = 1920 * Multiply by -2 -11x – 15y = -1860 12x + 15y = 1920 x= 60 small y = 80 large

II. Dependent and Inconsistent SystemsEx 1. Use elimination to solve the system. Check your solution.

2x + 5y = 12 2x + 5y = 15

** Multiply by – 1 to first equation

-2x – 5y = -12

2x + 5y = 15

0 = 3

Empty Set

Inconsistent

Parallel Lines (both equations have a slope of -2/5)

-8x + 4y = -2 4x – 2y = 1

-8x + 4y = - 2

8x - 4y = 2 Multiplied by 2

0 = 0

∞ Consistent Dependent

II. Dependent and Inconsistent SystemsEx 2. Use elimination to solve the system. Check your solution.

1. 5x - 3y = 8 10x – 6y = 18

Use elimination to solve the system. Check your solution.

2. 6x – 2y = 9 6x – 2y = 7

3. 4y + 30 = 10x 5x – 2y = 15

4. 5x + 3y = 2 2x + 20 = 4y

Writing ActivitiesWriting Activities

Homework

Integrated Algebra II- Section 3.2 Level A

Honors Algebra II- Section 3.2 Level B