SOLUTION: Hi! Use the elimination method to find all solutions of the system of equations. (Round each answer to two decimal places. Enter NONE in any unused answer blanks.) {x^2-y^2

Question 200163: Hi!

Use the elimination method to find all solutions of the system of equations. (Round each answer to two decimal places. Enter NONE in any unused answer blanks.)
{x^2-y^2=25
2x^2-y^2=x+55
thanks for the help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system

Multiply both sides of the first equation by -1

Distribute and multiply

Now add the two equations

Group like terms.

Combine like terms.

Get all terms to the left side.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

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 solutions (for the x values) are or

Now take each x value and plug them into either equation to solve for "y". Let me know if you need more help from here.

Note: In this case, you should get 4 ordered. However, one solution is repeated twice. So there are really only 3 ordered pair solutions.

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