Solving Systems of Linear Equations By Elimination with Multiplication

By: Janay Hunter & Dale Brown

Explanation of Topic

 The purpose of this topic is to use two or more equations to find a point where two lines meet/ intersect on a graph.

Example: Point you need to find  During this process you will get one of the following answers:  An X and a Y (x , y)  Lines intersect  A number equals a number -5 = -5  Lines touch all over  Different number equals each other 3 = 6  No solution/ parallel lines

Steps to Solving

 Check systems for any like coefficients.

3x + 4y = -25 2x – 3y = 6  If none multiply the whole equation by either coefficients.

3x + 4y = -25 2x – 3y = 6 2(3x + 4y = -25) 3(2x – 3y = 6) 6x + 8y = -50 6x – 9y = 18

Steps to Solving

(contd.)  Next you either add or subtract the equations, depending on the signs of similar coefficients then you perform a one step equation.

Will cancel 6x + 8y = -50 (-)6x – 9y = 18 (subtract everything)   17y = -68 17 17 y = -4 Plug found variable into one of the equations(your choice same answer either way) to find the other variable . And solve.

6x + 8(-4) = -5 6x + -32 = -5 simplify +32 +32 6x = 27 X = 4.5

6 6 Determine whether the systems intersect, parallel, or on top of each other

Practice Problems

1) 2x – y = 6 2) 2x + 7y = 1 3) 4x + 7y = 6 3x + 4y = -2 x + 5y = 2 6x + 5y = 20 ( , ) ( , ) ( , ) 4)9a – 2a = -8 5) x + y = 3 -7a + 3b = 12 2x – 3y= 16 ( , ) ( , )

Practice Problem

(contd.) 6) -5x + 3y = 6 7) 2x + y = 5 8) 12x – 3y = -3 x – y = 4 3x – 2y = 4 6x + y = 1 ( , ) ( , ) ( , ) 9) -4x + 2y = 0 10) 2x – 3y = 2 10x – 3y = 8 5x + 4y = 28 ( , ) ( , )

1. ( 2 , -2) 2. (-3, 1) 3. (5, -2) 4. (0 , 4) 5. (5, -2) Answers 6. ( -9 , -13) 7. (2, 1) 8. (0, 1) 9. (2, -4) 10.(4, 2 )

Study Tool

 Making It Simpler : follow the following steps to solve .

Solving Systems of Equations Using Elimination

Solve using Elimination: 4x + 2y = 14 7x 3y= 8 Are either variables opposites?

If yes, add equations.

If not multiply equations to make opposites, then add equations.

Solve the one variable equation Substitute to find other variable Check answer in the original equations 

it would have each step on a fold out piece of paper (able to print out)

Help Resources

 educational http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/study_gui de/pdfs/alg1_pssg_G056.pdf

http://webcache.googleusercontent.com/search?q=cache:rNv0pF50UAUJ:tea chers.henrico.k12.va.us/math/hcpsalgebra1/Documents/9 4/SolveSysByElimMult.ppt+solving+systems+of+equations+by+elimination +with+multiplication&cd=3&hl=en&ct=clnk&gl=us (link at top of page for the PowerPoint version)  Fun http://www.onlinem athlearning.com/systems-of-linear-equations-3.html

 Self – Test http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Systems%20of%20E quations%20Elimination.pdf