Finding the intersection of a circle and a line

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The text says:

On a single set of coordinate axes, sketch the line $x+16 = 7y$ and circle $x^2+y^2-4x+2y=20$ and find their points of intersection. Hint: eliminate x algebraically and solve the resulting quadratic equation in y.

I take the following steps:
Put the circle in standard form by completing the square:
$(x-2)^2 + (y+1)^2 = 25$
Rewrite the line equation in terms of x:
$x=7y-16$
Substitute x into the equation of the circle:
$(7y-16-2)+y+1=5$

Doing so gives me a value of $11/4$ for y. The text gives an answer of $(-2,2)$and $(5,3)$.

I've gone wrong somewhere but can't pinpoint exactly where.

Thanks in advance.

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You have changed the equation of the circle to a line equation, which is wrong.

$(7y-16-2)^2+(y+1)^2=5^2$