Answer
$(6,2)$
Work Step by Step
Multiply each equation (don't forget: both sides) as denoted:
$\left\{\begin{array}{ll}
5r-3s=24 & .../\times 5\\
3r+5s=28 & .../\times 3
\end{array}\right.$
$\left\{\begin{array}{ll}
25r-15s=120 & ...\\
9r+15s=84 & ...
\end{array}\right.\quad$ adding eliminates $s$
$34r=204$
$r=\displaystyle \frac{204}{34}=6$
Back-substitute into one of the initial equations:
$3r+5s=28$
$3(6)+5s=28$
$5s=28-18$
$5s=10$
$s=2$
Form an ordered pair $(r,s)$ as the solution to the system
$(6,2)$
