Simultaneous equations
From ACT Wiki
A set of related equations including two or more variables.
For 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.
For example:
y = 3z
z + y = 1
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.
