Answer
$(2.4, \pm2.4)$, $(-2.4, \pm2.4)$
Work Step by Step
Step 1. Rewrite the first equation as $x^2=16(1-\frac{y^2}{9})$ and plug it in the second equation to get
$\frac{16}{9}(1-\frac{y^2}{9})+\frac{y^2}{16}=1$. Multiply $16\times9^2$ on both sides to get
$9\times16^2-16^2y^2+9^2y^2=16^\times9^2$ or $175y^2=1008$
Step 2. Solve the above equation to get $y=\pm2.4$, back substitute into the first (or second) equation to get
$x^2=16(1-\frac{2.4^2}{9})$ or $x=\pm2.4$
Step 3. State the 4 intersection points: $(2.4, \pm2.4)$ and $(-2.4, \pm2.4)$
Step 4. Graph the equations and label the intersection points as shown.