Answer
$\left(-\frac{1}{2},\frac{3}{2}\right),\left(\frac{1}{2},\frac{3}{2}\right),\left(-\frac{1}{2},-\frac{3}{2}\right),\left(\frac{1}{2},-\frac{3}{2}\right)$.
Work Step by Step
The exercise allows any methods.
Use graphing method, see graphs of $7x^2-3y^2+5=0$ and $3x^2+5y^2=12$. We can identify the intersect(s) $\left(-\frac{1}{2},\frac{3}{2}\right),\left(\frac{1}{2},\frac{3}{2}\right),\left(-\frac{1}{2},-\frac{3}{2}\right),\left(\frac{1}{2},-\frac{3}{2}\right)$
Alternatively, one can isolate $y^2$ from the 2nd equation, plugin the 1st, then solve for $x$ first.
