How do you solve y=-x^2+4, y=1/2x+5 using substitution?
1 Answer
Aug 1, 2017
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]}
