Answer:
Our two intersection points are:

Step-by-step explanation:
We want to find where the two graphs given by the equations:

Intersect.
When they intersect, their <em>x-</em> and <em>y-</em>values are equivalent. So, we can solve one equation for <em>y</em> and substitute it into the other and solve for <em>x</em>.
Since the linear equation is easier to solve, solve it for <em>y: </em>
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Substitute this into the first equation:

Simplify:

Square. We can use the perfect square trinomial pattern:

Multiply both sides by 16:

Combine like terms:

Isolate the equation:

We can use the quadratic formula:

In this case, <em>a</em> = 25, <em>b</em> = -22, and <em>c</em> = -159. Substitute:

Evaluate:

Hence, our two solutions are:

We have our two <em>x-</em>coordinates.
To find the <em>y-</em>coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

And:

Thus, our two intersection points are:
