Solving Systems of Linear Equations

by graphing

Heather GreeneGrand Canyon UniversityTEC 542June 1, 2011

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What is a linear equation?

What is a system of linear equations?

Solving systems of linear equations by graphing

What is a linear equation?An equation with two variables for which the

graph of the solutions form a lineExample: y = 2x - 3There are many solutions for this equation. We

usually organize them in a t-chart:

x 2x - 3 y

0 2(0) - 3 -3

1 2(1) - 3 -1

2 2(2) - 3 1

3 2(3) - 3 3

Then we plot the (x,y) coordinates on a coordinate plane. Go to the next screen to

see! TABLE OF CONTENTS

x 2x - 3 y

0 2(0) - 3 -3

1 2(1) - 3 -1

2 2(2) - 3 1

3 2(3) - 3 3

What is a linear equation?

The (x,y) solutions form a line when graphed on a coordinate plane!

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What is a system of linear equations?Two or more linear equations that contain the

same variables.Example: y = 2x – 3

y = -x + 3

Follow this link to read about systems of equations:

http://www.purplemath.com

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x y

0 -3

1 -1

2 1

3 3

Solving systems of linear equations by graphing

The point where the two lines cross is the solution. That is the coordinate pair that makes both equations

true. The solution for this system of equations is (2,1).

y = 2x – 3 y = -x + 3

x y

0 3

1 2

2 1

3 0

y =

2x

– 3

y = -x +

3

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Solving systems of linear equations interactive tutorial

Follow this link to learn more about solving systems of equations, including what happens if you have parallel lines:

http://math123xyz.com

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