solve the nonlinear system y^2=x+1 and x+y=0

Question

solve the nonlinear equation with substitution or by elimination to find the solution set as an order pairs if any.

Answer 1

y^2 = x+1, x+y=0

x=-y

y^2 = -y+1

y^2+y -1 = 0

use the quadratic formula

y = -1/2 +/-.5sqr(1+4)

= -.5+.5sqr5, -5-.5sqr5

x=-y = .5-.5sqr5, 5+.5sqr5

solution set is (x,y)= (.5-.5sqr5, -.5+.5sqr5), (.5+.5sqr5, -.5-.5sqr5)

2 solutions

or use a graphing calculator and graph the parabola and line, then see the 2 points where they intersect