SOLUTION: Solve by substitution y^2=1+2x^2 x^2+2y^2=22 my options are (3,2),(3,-2), (-2,3), (-2,-3) (2,3), (2,-3), (-2,3), (-2,-3) (radical 7, radical 15) (-radical 7, radical 15) (ra

Question 254911: Solve by substitution
y^2=1+2x^2
x^2+2y^2=22
my options are
(3,2),(3,-2), (-2,3), (-2,-3)
(2,3), (2,-3), (-2,3), (-2,-3)
(radical 7, radical 15) (-radical 7, radical 15) (radical 7,-radical 15) (- radical 7, -radical 15)
(radical 15, radical 7) (radical 15, -radical 7)(-radical 15,radical 7, (-radical 15,-radical 7)
I am not getting any of these answers
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Plug in

Distribute

Subtract 22 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 "x":

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 solutions for 'x' are or

Now take each solution for 'x' and plug them into to find the corresponding 'y' solutions.

Let's find the corresponding solutions for y when

Start with the first equation.

Plug in (the first 'x' solution)

Square 2 to get 4.

Multiply

Add

Take the square root of both sides (don't forget the plus/minus)

or Break up the plus/minus

or Take the square root of 9 to get 3.

So when , we have two solutions for 'y' which are or . So we have two ordered pairs (2,3) and (2,-3)

--------------------------------------------------

Now let's find the corresponding solutions for y when

Start with the first equation.

Plug in (the second 'x' solution)

Square 2 to get 4.

Multiply

Add

Take the square root of both sides (don't forget the plus/minus)

or Break up the plus/minus

or Take the square root of 9 to get 3.

So when , we have two solutions for 'y' which are or . So we have two more ordered pairs (-2,3) and (-2,-3)

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Answer:

So the four ordered pair solutions are (2,3), (2,-3), (-2,3), and (-2,-3) which means that the answer is B)
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