Find all points where the circle x^2 + y^2 = 25 intersects the line x + 2 = 2y.
+128460 x^2 + y^2 = 25 x + 2 = 2y ⇒ x = 2y - 2
Sub the second equation into the first and we have that
(2y - 2)^2 + y^2 = 25 expand
4y^2 - 8y + 4 + y^2 = 25
5y^2 - 8y - 21 = 0 factor as
(5y + 7) (y - 3) = 0
Setting both factors to 0 and solving for y produces y = -7/5 and y = 3
And when y = -7/5, x = 2(-7/5) - 2 = -14/5 - 10/5 = -24/5
And when y = 3 , x =2(3) - 2 = 4
So....the intersecton points are ( -24/5, -7/5) and (4, 3)
