Simultaneous equations: Difference between revisions
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imported>Brianlenoach@hotmail.co.uk (Show solution and categorise page.) |
imported>Doug Williamson (Example rationalised to page standardisation for numerical examples) |
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A set of related equations including two or more variables. | A set of related equations including two or more variables. | ||
'''Example''' | |||
y = 3z ''and'' | y = 3z ''and'' | ||
| Line 8: | Line 9: | ||
'''Solution''' | |||
If the number of equations is at least as many as the number of variables, the equations can be solved. | If the number of equations is at least as many as the number of variables, the equations can be solved. | ||
Rearranging the second equation: | Rearranging the second equation: | ||
| Line 25: | Line 19: | ||
Substituting into the first equation, for z: | Substituting into the first equation, for z: | ||
y = 3 x (1 - y) | y = 3 x ( 1 - y ) | ||
y = 3 - 3y | y = 3 - 3y | ||
Revision as of 10:16, 7 April 2015
A set of related equations including two or more variables.
Example
y = 3z and
z + y = 1
Solution
If the number of equations is at least as many as the number of variables, the equations can be solved.
Rearranging the second equation:
z = 1 - y
Substituting into the first equation, for z:
y = 3 x ( 1 - y )
y = 3 - 3y
4y = 3
y = 0.75
z = 1 - 0.75
= 0.25
Check
y = 3z
= 3 x 0.25
= 0.75
OK.
z + y
= 0.25 + 0.75
= 1
OK too.
