Please Help Mathematic 9th grade

Question

The line with equation x-2y=1 intersects the curve(circle) with equation x²+y²-13 =0 at the points P and Q.

Find the coordinates of P and Q.

Answer 1

It's a line intersecting a circle in 2 points, in the 2nd and 4th quadrants

x-2y = 1

x = 2y+1

(2y+1)^2 + y^2 = 13

4y^2 + 4y + 1 + y^2 = 13

5y^2 + 4y -12 = 0 use quadratic formula

y = 1.2, -2

x = 3.4, -3

P = (-3,-2), Q = 3.4, 1.2) are the two intersection points of the line with the circle