# Simultaneous equations

From ACT Wiki

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.