Simultaneous equations: Difference between revisions
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A set of related equations including two or more variables. | A set of related equations including two or more variables. | ||
y = | '''Example''' | ||
x + y = 1 | |||
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. | |||
== See also == | == See also == | ||
* [[Equation]] | * [[Equation]] | ||
[[Category:Financial_management]] | |||
[[Category:Knowledge_and_information_management]] |
Latest revision as of 11:40, 13 May 2016
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.