6-3 & 6-4 Solving Systems by Elimination

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Presentation transcript:

6-3 & 6-4 Solving Systems by Elimination Goal: Solve systems of linear equations using elimination. Eligible Content: A1.1.2.2.1 / A1.1.2.2.2

Vocabulary Elimination Method – the process of adding two equations together to get a variable to cancel out. Also called the Linear Combinations Method. Opposites – two numbers that are the same distance from 0.

Steps Multiply one or both equations by any numbers that will give you opposite coefficients for a variable. Add the two equations together and solve for the remaining variable. Plug your answer from Step 2 into any equation to solve for the other variable. Write your answer as an ordered pair. Check your answer.

2x + 5y = 5 3x + 2y = -9 3 ( ) -2( ) 2x + 5y = 5 3x + 2y = -9 2x + 5 * 3 = 5 2x + 15 = 5 - 15 -15 2x = -10 2 2 x = -5 6x + 15y = 15 -6x – 4y = 18 11y = 33 11 11 y = 3 (-5, 3)

Let’s work on multiplying step only!! What would you multiply by for each problem? 2x + 3y = 9 and 4x + 4y = 10 –5x – 2y = 10 and 3x + 7y = 12 2x + y = 5 and 3x – 4y = 14 18x + 12y = 90 and 12x + 8y = 72

Examples 2x + 3y = 0 4x + 3y = 16 5x – 6y = 27 2x – 3y = 8 (3, -2) (6, 5) 4x + 3y = 16 2x – 3y = 8 (4, 0) –2x + 3y = 12 2x – 8y = –52 (6, 8) 3x + 5y = 6 –4x + 2y = 5 (-0.5, 1.5)

Use elimination to solve the system of equations Use elimination to solve the system of equations. 3x – 5y = 1 2x + 5y = 9 A. (1, 2) B. (2, 1) C. (0, 0) D. (2, 2)

Use elimination to solve the system of equations Use elimination to solve the system of equations. 9x – 2y = 30 x – 2y = 14 A. (2, 2) B. (–6, –6) C. (–6, 2) D. (2, –6)

Use elimination to solve the system of equations Use elimination to solve the system of equations. x + 7y = 12 3x – 5y = 10 A. (1, 5) B. (5, 1) C. (5, 5) D. (1, 1)

Use elimination to solve the system of equations Use elimination to solve the system of equations. 3x + 2y = 10 2x + 5y = 3 A. (–4, 1) B. (–1, 4) C. (4, –1) D. (–4, –1)

Practice x + 3y = 5 2x – 3y = 1 4x – 3y = 0 2x + 4y = –22 5x + 7y = 31 (2, 1) (-3, -4) (9, -2)

Homework Page 354 #8-12 even Page 360 #8-12 even