Simultaneous Equations

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  • 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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We need to multiply the second line by 2 (and then call this equation 3) so that we have the
same amount of x's on the top as on the bottom so that when we take the bottom line from
the top we eliminate x.
Therefore we have the following arrangement:
4x + 3y= 2...........(1)
4x + 2y = 0 ..........…read more

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