Question
How do you find the points of intersection, if any, of the equations:
x^2 + y^2 = 5
x - y = 1
x^2 + y^2 = 5
x - y = 1
Answers
MathMate
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.
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.