Question

What point is the intersection of the graphs of x2 + y2 = 25 and y = x + 7?

Answer 1

use substitution

x^2 + y^2 =25 is a circle with a centre at the origin and radius 5
y = x + 7 is a straight line with a y intercept at y = 7

then

x^2 + (x + 7)^2 = 25

now expand and simplify

x^2 + x^2 + 14x + 49 = 25

2x^2 + 14x + 24 = 0

2(x^2 + 7x + 12) = 0

which can be factorised to

2(x +3)(x+4) = 0

I'll leave you to find the 2 points where the curves intersect.