Answer
$\{(9,4)\}$
Work Step by Step
The system of equations are written as:
$3x-5y=7 ~~~(1) \\ 2x+3y=30 ~~~(2)$
Equation -(1) yields: $x=\dfrac{7+5y}{3} ~~~~(3)$
Plug $x=\dfrac{7+5y}{3} $ into the second equation and then solve for $y$ to obtain:
$2(\dfrac{7+5y}{3} )+3y=30 \\ \dfrac{19y}{3}=\dfrac{76}{3} \\ y=4$
Back substitution for $y=1$ in equation-3 to obtain:
$x=\dfrac{7+5(4)}{3} =9$
Solution set: $\{(9,4)\}$
