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# Solving Linear Systems By Combining Equations

Author: c o
##### Description:

This lesson teaches the student how to add and subtract linear equations.
Furthermore, it explains how to combine equations in order to solve linear systems.

The packet contains a short video presentation that covers the packet objectives. Supplemental exercises are also included.

(more)

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Tutorial

This presentation explains how to add and subtract linear equations, and how to use that technique to solve linear systems

## Supplemental Exercises

### Solve the following linear systems using the combination technique.  Hints are provided.

(solutions are provided at the bottom)

When approaching the following problems  you should look for a way to cancel out one of the variables.  Often getting variables to cancel involves multiplying an equation by a constant factor in order to make a coefficient in that equation equal the negative of the coefficient for the same variable in the other equation.

For example, if our two equations are

2x - y = 10

3x + 2y = 14

then we must choose a convenient factor.  Notice that in the first equation we have a -y and in the second we have 2y.  In this case, multiplying the first equation by 2 will give us a -2y in the first equation and a 2y in the second. Now the y terms will cancel.

4x - 2y = 20   (we multiplied 2 times 2x - y = 10)

3x + 2y = 14

adding these up gives us 7x + 0y  = 34.

To recap, you just need to get one of the variables to cancel out.  Choose a factor that will make one coefficient in one equation equal to the negative of that same coefficient in the other equation.  Now try these exercises, good luck.

1)

-x + y = 10

x - 2y = 12

(hint: just try adding the two together)

2)

3x + 2y = 5

6x - y = 20

(hint: multiply one of the equations by two before combining them)

3)

2x  + 5y = 4

3x + 2y = -5

(hint: multiply the top equation by 3 and the bottom equation by -2)

SOLUTIONS

1)  (x,y) = (-32,-22)

2) (x,y) = (3,-2)

3) (x,y) = (-3,2)

Source: Colin O'Keefe

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