SOLUTION: Hi! Use the substitution method to find all solutions of the system of equations. (Round each answer to two decimal places.) {2x^2+4y=11 x^2-y^2=1/2 thanks for the homew

Question 200162: Hi!
Use the substitution method to find all solutions of the system of equations. (Round each answer to two decimal places.)
{2x^2+4y=11
x^2-y^2=1/2
thanks for the homework help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Add to both sides.

Move back to the first equation.

Plug in

Distribute

Subtract 11 from both sides.

Combine like terms.

Notice that the quadratic is 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 .

Simplify the square root

or Break up the expression.

or Reduce

So the solutions (for "y") are or

which approximate to or

Now plug these values into to find the corresponding "x" values.

Note: You should get four ordered pair solutions (there are two x values for each y value you just found).

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