How do you solve x+y=3 and x = 4-(y-1)^2?

1 Answer
Apr 9, 2016

(x,y)=(0,3)
or
(x,y)=(3,0)

Explanation:

If x+y=3
then y=3-x

and we can substitute (color(red)(3-x)) in place of y in the second equation: x=4-(y-1)^2

This gives
color(white)("XXX")x=4-(color(red)(3-x)-1)^2

color(white)("XXX")x=4-(2-x)^2

color(white)("XXX")x=4-(4-4x+x^2)

#color(white)("XXX")x= 4x-x^2

color(white)("XXX")3x-x^2=0

color(white)("XXX")x(3-x)=0

color(white)("XXX")rarr x=0color(white)("XX")orcolor(white)("XX")x=3

If x=0 then x+y=3 rarr y=3

If x=3 then x+y=3 rarr y=0