Answer
$(3, 4)$ and $(-3, 4)$
Work Step by Step
With the elimination method, we can see that the $x^{2}$ term can be eliminated.
$x^{2} - 2y = 1$
$x^{2} + 5y = 29$
We subtract the second equation from the first equation to get:
$-7y = - 28$
Solve for $y$ by dividing both sides by $-7$:
$y = 4$
Now that we have the value for $y$, we can plug it into one of the equations to solve for $x$:
$x^{2} - 2(4) = 1$
$x^{2} - 8 = 1$
Add $8$ on both sides:
$x^{2} = 9$
Take the square root of both sides to get:
$x = 3$ or $x = -3$
We now know that there are two points where these equations intersect, which are $(3, 4)$ and $(-3, 4)$.
