Welcome back…. Let’s warm up! 1) 4x + 5y = 12 2) 3x – 2y = 12 4x + 3y = 4 4x + 2y = 2.

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Presentation transcript:

Welcome back…. Let’s warm up! 1) 4x + 5y = 12 2) 3x – 2y = 12 4x + 3y = 4 4x + 2y = 2

8-4 Elimination Using Multiplication Objective: To solve systems of equations using the Elimination method with Multiplication **Let’s use whiteboards today!

Example 1 – on paper 2x + y = 5 3x – 2y = 4 7x = 14 x = 2 2(2) + y = y = 5 y = 1 ( ) 2= 4x + 2y = 10 3x – 2y = 4 ANSWER: (2,1)

On a white board!! 1) -3x – 4y = 2 -2x + y = -6 Answers: 1. (2,-2) 2. (5,-2) 3. Infinitely Many 2) 3x – 2y = 19 5x + 4y = 17 3) x – 2y = -1 -2x + 4y = 2

Example 2 – on paper 0 = -y + 4 y = 4 3x = 2(4) – 2 3x = 8 – 2 3x = 6 x = 2 ( ) -3= -9x = -6y + 6 9x = 5y – 2 ANSWER: (2,4) 9x = 5y – 2 3x = 2y – 2

EXAMPLE 3 – on whiteboard 2x – 3y = 2 5x + 4y = 28 What do we eliminate? y! 2(4) – 3y = 2 8 – 3y = 2 -3y = -6 y = 2 8x – 12y = 8 15x + 12y = 84 23x = 92 x = 4 ANSWER (4,2) ( )4 ( )3

EX4: 2x + 3y = 5 5x + 4y = 16 Eliminate x 1 st times 5 2 nd times -2 10x + 15y = x – 8y = -32 7y = -7 y = -1 Eliminate y 1 st times 4 2 nd times -3 8x + 12y = x – 12y = x = -28 x = 4 Answer: (4,-1)

Try with a mathlete: 1) 3x + 5y = 11 2x + 3y = 7 2) 2x – 3y = 8 -5x + 2y = 13

Homework: Pg. 479 # 15 – 31 odd

Math Lab Systems of Equations Review **Let’s use whiteboards today!

Substitution 1) y = 3x x + 2y = -21 Answers: 1) (-3,-9) 2) (3,0) 2) y = 2x – 6 3x + 2y = 9

Elimination 1) -3x + 4y = 122) x + y = 8 3x – 6y = 18 x – y = 4 (-24,-15) (6,2)

Elimination with Multiplication 1) -3x – 4y = 2 -2x + y = -6 Answers: 1. (2,-2) 2. Infinitely Many 2) x – 2y = -1 -2x + 4y = 2

Elimination with Multiplication 1) 4x + 3y = 19 3x – 4y = 8 Answer: (4,1) 2) 4x – 7y = 10 3x + 2y = -7 Answer: (-1,-2)

Even More Practice Solve using any method: Shall we race?? 1) 7x + 3y = -1 4x + y = 3 2) 3x + 4y = 10 6x + 8y = 5 3) x – y = 2 2x – 3y = 5