Question

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

Answer 1

`(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`