Warm Up Use elimination to solve. 2m – 3n = 14 m + 3n = -11

7-4 Elimination Using Multiplication Objective: Solve systems of equations by using elimination with multiplication. December 4, 2009

If neither variable can be eliminated by simply adding or subtracting the equations, use the Multiplication Property of Equality so that adding or subtracting eliminates one of the variables.

Examples: Solve. 1. 2x + y = 23 3x + 2y = 37

2.2x + y = 5 3x – 2y = 4

3. 4x – 3y = 12 x + 2y = 14

4.7x + 3y = -1 4x + y = 3

5.

For some systems of equations, it is necessary to multiply each equation by a different number in order to solve the system by elimination. You can choose to eliminate either variable.

Examples: Solve. 1. 4x + 3y = 8 3x – 5y = -23

2. 4x + 3y = 19 3x – 4y = 8

3. 4x + 7y = 6 6x + 5y = 20

4.2x + 2y = 24 3x – 3y = 24

5.3x – 2y = -7 2x – 5y = 10

Solving Systems of Equations Review MethodThe Best Time to Use GraphingTo estimate the solution SubstitutionIf one of the variables in either equation has a coefficient of 1 Elimination Using AdditionIf one of the variables has opposite coefficients in the two equations Elimination Using SubtractionIf one of the variables has the same coefficient in the two equations Elimination Using MultiplicationIf none of the coefficients are 1 and neither of the variables can be eliminated by simply adding or subtracting.

Classwork – Workbook page 50 #1 – 9, 12 – 17 Homework - page 391 #13 – 24