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Solving System of Equations By Elimination

Using Addition

Two equations together are called a system of equations. Sometimes adding the two equations will eliminate one variable.

Example:

3x - 7y = 24

2x + 7y = 6

Add the two equations:

5x = 30

x = 6

y = - 6/7

Using Subtraction

Sometimes subtracting two equations will eliminate one variable.

Example:

5a + 2b = 8

9a + 2b = 6

Subtract the two equations:

- 4a = 2

a = - 1/2

b = 21/4

Using Multiplication

Sometimes multiplying one equation by a number will result in the coefficient of one variable being the inverse of the coefficient of the same variable in the other equation.

Example:

2x - 4y = 16

5x + 2y = 4

Multiply the second equation by 2:

10x + 4y = 8

Now add the first equation:

12x = 24

x = 2

y = - 3

Example 2 - multiply both equations by a number:

3x - 4y = 8

2x - 3y = 12

Multiply the first equation by 3:

9x -12y = 24

Multiply the second equation by - 4:

- 8x +12y = - 48

Add the two resulting equations:

x = - 24

y = - 20

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