SOLUTION: Hello, can you please help me solve this problem. --Solve the system by using the substitution method-- {{{x^2+y^2=113}}} with this under it {{{x-y=1}}}

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Question 191381: Hello, can you please help me solve this problem.
--Solve the system by using the substitution method--
x%5E2%2By%5E2=113 with this under it x-y=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x-y=1 Start with the second equation.


x=y%2B1 Add "y" to both sides.


x%5E2%2By%5E2=113 Move onto the first equation


%28y%2B1%29%5E2%2By%5E2=113 Plug in x=y%2B1


y%5E2%2B2y%2B1%2By%5E2=113 FOIL


y%5E2%2B2y%2B1%2By%5E2-113=0 Subtract 113 from both sides.


2y%5E2%2B2y-112=0 Combine like terms.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=2, b=2, and c=-112


Let's use the quadratic formula to solve for y


y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


y+=+%28-%282%29+%2B-+sqrt%28+%282%29%5E2-4%282%29%28-112%29+%29%29%2F%282%282%29%29 Plug in a=2, b=2, and c=-112


y+=+%28-2+%2B-+sqrt%28+4-4%282%29%28-112%29+%29%29%2F%282%282%29%29 Square 2 to get 4.


y+=+%28-2+%2B-+sqrt%28+4--896+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-112%29 to get -896


y+=+%28-2+%2B-+sqrt%28+4%2B896+%29%29%2F%282%282%29%29 Rewrite sqrt%284--896%29 as sqrt%284%2B896%29


y+=+%28-2+%2B-+sqrt%28+900+%29%29%2F%282%282%29%29 Add 4 to 896 to get 900


y+=+%28-2+%2B-+sqrt%28+900+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


y+=+%28-2+%2B-+30%29%2F%284%29 Take the square root of 900 to get 30.


y+=+%28-2+%2B+30%29%2F%284%29 or y+=+%28-2+-+30%29%2F%284%29 Break up the expression.


y+=+%2828%29%2F%284%29 or y+=++%28-32%29%2F%284%29 Combine like terms.


y+=+7 or y+=+-8 Simplify.


So the answers for "y" are y+=+7 or y+=+-8



Now take these solutions and plug them into x=y%2B1 to find "x"

x=y%2B1=7%2B1=8

So when x=8, y=7


x=y%2B1=-8%2B1=-7

So when x=-7, y=-8



So the solutions as ordered pairs are (8,7) or (-7,-8)