Question

How do you find the points of intersection, if any, of the equations:

x^2 + y^2 = 5
x - y = 1

Answer 1

You would solve for one of the unknowns using the linear equation (x-y=1 => x=y+1)

and substitute into the quadratic equation, and solve for the only unknown, y.
(y+1)^2+y^2=5
y^2+y-2=0
y=1 or -2
Now substitute y=1 or -2 into the linear equation to get the corresponding values of x. This will complete the solution of two intersection points.