Find the coordinates of the point(s) of intersection of the line y = 2x + 5 with the circle (x - 3)^2 + (y + 4)^2 = 50.
Well you have two equations and two unknowns. Start by plugging in y = 2x + 5 into the other equation, like this:
$\displaystyle (x - 3)^2 + ({\color{red}2x + 5} + 4)^2 = 50$.
Solve for x, and when you're done, plug that back into y = 2x + 5 to solve for y. (You may get two answers for x, so plug each answer in to get a different y.)
01
(x - 3)^2 + (2x + 5 + 4)^2 = 50
(x - 3)^2 + (2x + 9)^2 = 50
x^2 - 6x + 9 + 4x^2 + 36x + 81 = 50
5x^2 + 30x + 90 = 50
5x^2 + 30x + 40 = 0
Using the quadratic formula:
x = -2 or x = -4
y = 2 (-2) + 5
= 1
or
y = 2(-4) + 5
= -3
Am I right so far? If so, what do I do next?