Simultaneous equations

From ACT Wiki
Jump to navigationJump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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.


See also