Question

What is one of the solutions to the following system of equations? Y2+X2=65
Y+x=7

Answer 1

x+y=7
minus x from both sides
y=7-x
subsitute 7-x for y

(7-x)²+x²=65
x²-14x+49+x²=65
2x²-14x+49=65
minus 65 both sides
2x²-14x-16=0
undistribute 2
2(x²-7x-8)=0
factor
what 2 numbers muliply to get -8 and add to get -7
-8 and 1
2(x-8)(x+1)=0
set to zero

x-8=0
x=8

x+1=0
x=-1

x=8 and -1

sub back

y=7-x

for x=8
y=7-8
y=-1
(8,-1) is a solution

for x=-1
y=7-(-1)
y=7+1
y=8
(-1,8) is the other solution


(8,-1) and (-1,8) are the solutions



so that is the first option