Question

What are the solutions to the system of equations?
x^2+y^2=5
y=2x

Answer 1

we can substitute y=2x in the quadratic equation to get:

x^2+(2x)^2=5

x^2+4x^2=5

5x^2=5

x^2=1

x=±1 so there are two solutions when x=-1 and 1, using y=2x we get the corresponding y values...

y(-1)=-2 and y(1)=2 so the two solutions are the two points:

(-1,-2) and (1,2)