Answer
$\left(\frac{1}{2},\frac{4}{3}\right),\left(2,\frac{1}{3}\right)$.
Work Step by Step
The exercise allows any method.
Use graphing method, see graphs of $4x^2-3xy+9y^2=15$ and $2x+3y=5$. We can identify the intersect(s) $\left(\frac{1}{2},\frac{4}{3}\right),\left(2,\frac{1}{3}\right)$.
Alternatively, one can isolate $y$ in the 2nd equation, plugin the 1st to solve for $x$, then $y$.
