Kitty Korner

Hi my name is Allison and welcome to my webpage, Kitty Korner. Here you will learn how to solve systems of linear equations. When you are done, I"m sure you will be ready to pounce on any problem that comes your way!

One way to solve linear equations is through substitution. Here is an example:

3x+ 4y = -4

x + 2y = 2

1. Solve the second equation for x like so:

x = -2y + 2

2. Then substitute the new equation into the x place in the the first equation3. Next subsitute the y into the first problem and solve for x.

3( -2y +2) +4y = -4

-6y + 6 +4y = -4

6 - 2y = -4

-2y = -10

y = 5

3. Next subsitute the y into the first problem and solve for x.

3x + 4 (5) = -4

3x + 20 = -4

3x = -24

x = -8

Therefore, the solution the the system of linear equations is:

(-8, 5)

Another way to solve systems of linear equations is through linear combination. Here is a example:

2x - 4y = 13

4x - 5y = 8

1. First we will multiply the first equation by -2. This will make the x's cancel.

-4x + 8y = -26

2. Then we will combine the 2 new equations and solve for y.

3y = -18

y = -6

3. Now we will subsitute the value for y into the first equation and solve for x.

2x - 4(-6) = 13

2x + 24 = 13

2x = -11

x = -11/2

Therefore the solution for the system of linear equations is:

(-11/2, -6)

A third way to solve systems of linear equations is through graphing. Here is an example:

2x - y = 1

x + y = 3

1. First, we must put the two equations in slope intercept form.

y = 2x - 1

y = -x + 3

2. Then use the y intercept and the slope to graph your equations.

The solution to the system of linear equations is (2,1)

Visit these webpages for more math help:

Purplemath - Your Algebra Resource

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