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}}}

Question 191381: Hello, can you please help me solve this problem.
--Solve the system by using the substitution method--
with this under it
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Add "y" to both sides.

Move onto the first equation

Plug in

FOIL

Subtract 113 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for y

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the answers for "y" are or

Now take these solutions and plug them into to find "x"

So when ,

So when ,

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