Answer
$(-2,-1)$, $(-2,1)$, $(2-1)$, $(2,1)$
Work Step by Step
Here, we have $3(3x^2+4y^2-16)=(3)(0) \implies 9x^2+12y^2-48=0$ ....(1)
and $4(2x^2-3y^2-5)=(4)(0) \implies 8x^2-12y^2-20=0$ ...(2)
After adding the above two equations, we get
$17x^2-68 =0$
This gives: $x^2=4 \implies x=-2,2$
when $x=2$ then we have $3(2)^2+4(2)^2-16=0 \implies y^2=1$
This gives: $y=1, -1$
when $x=-2$ then we have $3(-2)^2+4(-2)^2-16=0 \implies y^2=1$
This gives: $y=1, -1$
Hence, our answers are: $(-2,-1)$, $(-2,1)$, $(2-1)$, $(2,1)$
