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

Algebra ->  Systems-of-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B2y%5E2=22 Start with the second equation.


x%5E2%2B2%281%2B2x%5E2%29=22 Plug in y%5E2=1%2B2x%5E2


x%5E2%2B2%2B4x%5E2=22 Distribute


x%5E2%2B2%2B4x%5E2-22=0 Subtract 22 from both sides.


5x%5E2-20=0 Combine like terms.


Notice that the quadratic 5x%5E2-20 is in the form of Ax%5E2%2BBx%2BC where A=5, B=0, and C=-20


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%285%29%28-20%29+%29%29%2F%282%285%29%29 Plug in A=5, B=0, and C=-20


x+=+%280+%2B-+sqrt%28+0-4%285%29%28-20%29+%29%29%2F%282%285%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0--400+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-20%29 to get -400


x+=+%280+%2B-+sqrt%28+0%2B400+%29%29%2F%282%285%29%29 Rewrite sqrt%280--400%29 as sqrt%280%2B400%29


x+=+%280+%2B-+sqrt%28+400+%29%29%2F%282%285%29%29 Add 0 to 400 to get 400


x+=+%280+%2B-+sqrt%28+400+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%280+%2B-+20%29%2F%2810%29 Take the square root of 400 to get 20.


x+=+%280+%2B+20%29%2F%2810%29 or x+=+%28-0+-+20%29%2F%2810%29 Break up the expression.


x+=+%2820%29%2F%2810%29 or x+=++%28-20%29%2F%2810%29 Combine like terms.


x+=+2 or x+=+-2 Simplify.


So the solutions for 'x' are x+=+2 or x+=+-2


Now take each solution for 'x' and plug them into y%5E2=1%2B2x%5E2 to find the corresponding 'y' solutions.


Let's find the corresponding solutions for y when x=2


y%5E2=1%2B2x%5E2 Start with the first equation.


y%5E2=1%2B2%282%29%5E2 Plug in x=2 (the first 'x' solution)


y%5E2=1%2B2%284%29 Square 2 to get 4.


y%5E2=1%2B8 Multiply


y%5E2=9 Add


y=%22%22%2B-sqrt%289%29 Take the square root of both sides (don't forget the plus/minus)


y=sqrt%289%29 or y=-sqrt%289%29 Break up the plus/minus


y=3 or y=-3 Take the square root of 9 to get 3.


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

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Now let's find the corresponding solutions for y when x=-2


y%5E2=1%2B2x%5E2 Start with the first equation.


y%5E2=1%2B2%282%29%5E2 Plug in x=-2 (the second 'x' solution)


y%5E2=1%2B2%284%29 Square 2 to get 4.


y%5E2=1%2B8 Multiply


y%5E2=9 Add


y=%22%22%2B-sqrt%289%29 Take the square root of both sides (don't forget the plus/minus)


y=sqrt%289%29 or y=-sqrt%289%29 Break up the plus/minus


y=3 or y=-3 Take the square root of 9 to get 3.


So when x=-2, we have two solutions for 'y' which are y=3 or y=-3. 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)