How do you find the exact solutions to the system $y^2+x^2=9$ and $y=7-x$ ?

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Answer 1 · 2016-10-28T13:21:34

We can substitute equation $2$ directly into equation $1$ .

$y = 7 - x -> (7 - x)^2 + x^2 = 9$

$49 - 14x + x^2 + x^2 = 9$

$2x^2 - 14x + 40 = 0$

$2(x^2 - 7x + 20) = 0$

$x^2 - 7x + 20 = 0$

$x = (-b +- sqrt(b^2 - 4ac))/(2a)$

$x = (-(-7) +- sqrt(-7^2 - 4(1)(20)))/(2(1))$

$x= (7 +- sqrt(-31))/2$

$x = O/$

Hence , this system has no real intersection points.

Hopefully this helps!

How do you find the exact solutions to the system y^2+x^2=9y^2+x^2=9 and y=7-xy=7-x?