How do you solve the system #x^2+y^2=7# and #y=x-7#?
1 Answer
Oct 21, 2016
There is no solution.
Explanation:
We can use the fact that
#x^2+color(red)y^2=7" "=>" "x^2+color(blue)((x-7))^2=7#
Expanding the resultant equation and then solving it:
#x^2+(x^2-14x+49)=7#
#2x^2-14x+42=0#
Dividing through by
#x^2-7x+21=0#
Examining this, we see that the discriminant
We can graph the two equations given originally:
graph{(x^2+y^2-7)(y-x+7)=0 [-19.64, 20.92, -13.17, 7.1]}
The two graphs never intersect, so this confirms our conclusion of no solution.