Answer
$\{(\dfrac{1}{3},\dfrac{1}{2})\}$
Work Step by Step
The system of equations are written as:
$3x-2y=0 ~~~(1) \\ 9x+8y=7 ~~~(2)$
Equation -(1) yields: $x=\dfrac{2y}{3} ~~~~(3)$
Plug $x=\dfrac{7+5y}{3} $ into the second equation and then solve for $y$ to obtain:
$9(\dfrac{2y}{3})+8y=7 \\ 14y=7\\ y=\dfrac{1}{2}$
Back substitution for $y=\dfrac{1}{2}$ in equation-3 to obtain:
$x=\dfrac{2}{3}\times \dfrac{1}{2} =\dfrac{1}{3}$
Solution set: $\{(\dfrac{1}{3},\dfrac{1}{2})\}$
