Simultaneous equations: Difference between revisions

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.

@@ Line 1: / Line 1: @@
 A set of related equations including two or more variables.
-For example:
-y = 3x ''and''
+'''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
+y = 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 ==
 * [[Equation]]
+[[Category:Financial_management]]
+[[Category:Knowledge_and_information_management]]