Question

How do you solve the system `x^2+y^2=20` and `y=x-4`?

Answer 1

`x=2+-sqrt6`

Explanation:

Since we are given y in terms of x, we can substitute directly into the other equation.

`rArrx^2+(x-4)^2=20larr" equation in one variable"`

`rArrx^2+x^2-8x+16-20=0larr" quadratic equation"`

`rArr2x^2-8x-4=0`

divide both sides by 2

`x^2-4x-2=0`

To solve use the `color(blue)"quadratic formula"`

with `a=1,b=-4,c=-2`

`rArrx=(4+-sqrt24)/2=(4+-2sqrt6)/2=2+-sqrt6`