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Solving Linear Systems of Equations by Elimination

Helpful Strategies When Using Elimination

Different linear systems may require different strategies for eliminating one of the variables.

1. In some linear systems, a variable can be eliminated simply by adding the equations.

Add the equations to eliminate y.

There is no need to multiply either equation by a constant.

4x

-x

-

+

3y

3y

=

=

-

 

19

16

3x + 0y = - 3

2. In a system that contains fractions, multiply both sides of an equation by the LCD of its fractions to clear the fractions and make the system easier to work with.

To clear the fractions in the first equation, multiply both sides by 15, the LCD of and .

Multiply both sides of the first equation by 15.

 

Do not change the second equation. Add the equations to eliminate y.

3. In some systems, only one equation needs to be multiplied by a constant.

Eliminate x.  5x - 7y

15x + 8y

= -33 

=17

Multiply both sides of the first equation by -3. Do not change the second equation.

Add the equations to eliminate x

The solution of the system is (-1, 4).

4. In some systems, both equations must be multiplied by a constant.

Eliminate x. -2x + 11y

3x - 5y

= -28

= 19

Multiply both sides of the first equation by 3.

 Multiply both sides of the second equation by 2.

Add the equations to eliminate x.

The solution of the system is (3, -2).

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