How do you solve the system x2+y2=7 and y=x−7?
1 Answer
Oct 21, 2016
There is no solution.
Explanation:
We can use the fact that
x2+y2=7 ⇒ x2+(x−7)2=7
Expanding the resultant equation and then solving it:
x2+(x2−14x+49)=7
2x2−14x+42=0
Dividing through by
x2−7x+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.
