[tex] \left[\begin{array}{ccc}ax+by=r\\\\-bx+cy=s\end{array}\right] [/tex]
Isolate x for [tex]ax+by=r[/tex]
[tex]x= \frac{r-by}{a} ; a \neq 0[/tex]
Subsititute [tex]x= \frac{r-by}{a} [/tex]
[tex]-b \frac{r-by}{a} +cy=s[/tex]
Isolate r for : [tex]-b \frac{r-by}{a}+cy=s[/tex]
[tex]r=- \frac{as-acy-b^2y}{b} ; a \neq 0;b \neq 0[/tex]
For x : [tex] \frac{r-by}{a} [/tex]
Subsititute r = [tex]- \frac{as-acy-b^2y}{b} [/tex]
[tex]x= -\frac{as-acy-b^2y}{b}/a[/tex]
[tex]x = \frac{cy-s}{b} [/tex]
The solutions to the system of equations are:
[tex]r= -\frac{as-acy-b^2y}{b}[/tex] and [tex]x = \frac{cy-s}{b} [/tex]
hope this helps!
