Question

How do you solve the system `x^2+y^2=25` and `y=-3`?

Answer 1

`color(green)((x,y)=(-4,-3))` and `color(green)((x,y)=(+4,-3))`

Explanation:

If `color(blue)x^2+color(red)y^2=25`
and `color(red)y=color(red)(-3)`
then
`color(white)("XXX")color(blue)x^2+(color(red)(-3))^2=25`

`color(white)("XXX")color(blue)x^2+9=25`

`color(white)("XXX")color(blue)x^2=16`

`color(white)("XXX")color(blue)x=+-4`