How do you solve #y=-x^2+4, y=1/2x+5# using substitution?

1 Answer
Aug 1, 2017

#"no solution"#

Explanation:

#color(red)(y)=-x^2+4to(1)#

#color(red)(y)=1/2x+5to(2)#

#"since both equations express y in terms of x we can"#
#"equate them"#

#rArr1/2x+5=-x^2+4#

#"rearrange and equate to zero"#

#rArrx^2+1/2x+1=0#

#"check the nature of the roots using the "color(blue)"discriminant"#

#Delta=b^2-4acrarr(a=1,b=1/2,c=1)#

#color(white)(xx)=1/4-4<0#

#"hence there are no real solutions"#

#"that is the line and parabola do not intersect"#
graph{(y+x^2-4)(y-1/2x-5)=0 [-20, 20, -10, 10]}