Solve each system graphically

Question

Y^2 - x^2 = 24 and y = 3x - 8

Answer 1

y^2 = x^2 + 24 = (3x-8)^2 = 9x^2 -48x + 64

8x^2 - 48x + 64 = 0

divide by 8

x^2 -6x + 5 = 0

factor

(x_5)(x-1) = 0

set each factor = 0

x = 1, 5

the graphs are a straight line intersecting a hyperboa in 2 points

(1, -5) and (5,0)