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:

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

Point you need to find

Steps to Solving

Check systems for any like coefficients.3x + 4y = -252x – 3y = 6

If none multiply the whole equation by either coefficients.

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

2x – 3y = 6 3(2x – 3y = 6) 6x – 9y = 18

Step: 1

Step: 2

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.

6x + 8y = -50 (-)6x – 9y = 18 17y = -68 17 17 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 +32 +32 6x = 27 6 6 Determine whether the systems intersect, parallel, or on top of each other

Will cancel

y = -4

(subtract everything)

simplify

X = 4.5

Step: 3

Step: 4

Step: 5

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 ( , ) ( , )

Answers

1. ( 2 , -2)2. (-3, 1)3. (5, -2)4. (0 , 4)5. (5, -2)

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 EliminationSolve using Elimination:

4x + 2y = 147x 3y= 8

Are either variables opposites?If yes, add equations.

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

Solve the one variable equationSubstitute 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 educationalhttp://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/study_guide/pdfs/alg1_pssg_G056.pdf

http://webcache.googleusercontent.com/search?q=cache:rNv0pF50UAUJ:teachers.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 – Testhttp://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Systems%20of

%20Equations%20Elimination.pdf