\(\left[\begin{array}{ccc}ax+by=r\\\\-bx+cy=s\end{array}\right]\)
Isolate x for \(ax+by=r\)
\(x= \frac{r-by}{a} ; a
eq 0\)
Subsititute \(x= \frac{r-by}{a}\)
\(-b \frac{r-by}{a} +cy=s\)
Isolate r for : \(-b \frac{r-by}{a}+cy=s\)
\(r=- \frac{as-acy-b^2y}{b} ; a
eq 0;b
eq 0\)
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!
