# Simultaneous Equations

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- Created by: Bhavik
- Created on: 05-06-11 16:14

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Simultaneous Equations

Simultaneous equations are two equations containing two unknown values (usually x and y).

These can be found by combining the equations in some way.

Worked examples

Consider the following simultaneous equation:

2x + 2y = 10 ............(1)

2x + y = 7 .............(2)

Subtracting (2) from (1) to eliminate x

0 + y = 3

y = 3

substituting for y into (1)

2x + 2(3) = 10

2x + 6 = 10

2x = 4

x = 2

Consider this second simultaneous equation

3x + 2y = 10 .........(1)

x 2y = 6 ..........(2)

Adding (1) and (2) to eliminate y

4x + 0 = 16

4x = 16

x = 4

Substituting for x into (1)

3(4) + 2y = 10

2y = 1012

2y = 2

y = 1

Consider this last example

4x + 3y = 2 .............(1)

2x + y = 0 ..............(2)

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