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!