Question

Elimination method: ax+by=r, -bx+cy=s

Answer 1

$\left[\begin{array}{ccc}ax+by=r\\\\-bx+cy=s\end{array}\right]$

Isolate x for $ax+by=r$

$x= \frac{r-by}{a} ; a \neq 0$

Subsititute $x= \frac{r-by}{a}$

$-b \frac{r-by}{a} +cy=s$

Isolate r for : $-b \frac{r-by}{a}+cy=s$

$r=- \frac{as-acy-b^2y}{b} ; a \neq 0;b \neq 0$

For x : $\frac{r-by}{a}$

Subsititute r = $- \frac{as-acy-b^2y}{b}$

$x= -\frac{as-acy-b^2y}{b}/a$

$x = \frac{cy-s}{b}$

The solutions to the system of equations are:

$r= -\frac{as-acy-b^2y}{b}$ and  $x = \frac{cy-s}{b}$

hope this helps!