1. ## Help solving equations please

I am working through an old book and an example has these two equations that need to be used to solve for x and y:
xm + y = m
x + yn = n

The solution has x = (mn - n) / (mn - 1 ) and y = (mn - m) / (mn - 1).
I keep getting the wrong answer!

Thanks,
Ultros

2. Hello, Ultros88!

There are several ways to solve this system.
I'll use "Elimination" . . .

$\begin{array}{cccc}mx + y &=& m & {\color{blue}[1]}\\ x + ny &= &n & {\color{blue}[2]}\end{array}$

The solution is: . $\begin{array}{ccc} x& =&\dfrac{mn - n}{mn - 1} \\ \\[-3mm] y &= &\dfrac{mn - m}{mn - 1} \end{array}$

$\begin{array}{cccccc}\text{Multiply {color{blue}[1]} by }n\!: & mnx &+& ny &=& mn \\ \text{Subtract {\color{blue}[2]}:} & x &+& ny &=& n \end{array}$

And we have: . $mnx - x \;=\;mn - n \quad\Rightarrow\quad x(mn-1) \;=\;mn - n$

. . Therefore: . $\boxed{x \;=\;\frac{mn-n}{mn-1}}$

$\begin{array}{cccccc}\text{Multiply {color{blue}[2]} by }m\!: & mx &+& mny &=& mn \\ \text{Subtract {\color{blue}[1]}:} & mx &+& y &=& m \end{array}$

And we have: . $mny - y \:=\:mn - m \quad\Rightarrow\quad y(mn-1) \:=\:mn-m$

. . Therefore: . $\boxed{ y \;=\;\frac{mn-m}{mn-1}}$