You can solve the equations by equating the y's and then substituting for each y.
color(red)(y = sqrtx) color(white)(xxxx)and " "color(blue)(y = x-6)y=√x××and y=x−6
color(white)(xxxxxxxxx) color(red)(y) = color(blue)(y)××××xy=y
Therefore..color(red)( sqrtx) = color(blue)(x-6)" "larr√x=x−6 ← only x terms
(sqrtx)^2 = (x-6)^2 " "larr(√x)2=(x−6)2 ← square both sides.
x = x^2 -12x +36" "larrx=x2−12x+36 ← make the quadratic = 0
x^2 -13x + 36 = 0" "larrx2−13x+36=0 ← factorize
Find factors of 36 which ADD to 13. Signs are both negative.
(x-9)(x-4) = 0(x−9)(x−4)=0
If x-9 = 0 rarr x = 9" "x−9=0→x=9 OR If " "x-4 =0 rarr x = 4 x−4=0→x=4
Now find y.
color(red)(y = sqrtx) color(white)(xxxx)and " "color(blue)(y = x-6)y=√x××and y=x−6
y = sqrt 9 = 3" "larry=√9=3 ← only the principal square root was indicated
y=sqrt4 = 2y=√4=2
y = x-6 rarr y = 9-6 = 3y=x−6→y=9−6=3
y = x-6 rarr y = 4-6 = -2y=x−6→y=4−6=−2
