Question

Find all solutions of the system of equations. Order your answers from smallest to largest x, then from smallest to largest y.)

x^2 + y2= 53
x2− y2= 3

Answer 1

draw a picture of the circle with center at origin and radius 3.8
then the hyperbola x^2-y^2 = 3
it hits the x axis at -sqrt 3 and + sqrt 3 and opens right and left
so it crosses the circle once in each of the 4 quadrants

add equations
2 x^2 = 56
x^2 = 28
x =+/- 2 sqrt 7
y^2 = 25
y = +/-5
so
(2sqrt7 , 5)
(2sqrt7 , -5)
(-2sqrt7, 5)
(-2sqrt7, -5)