document.write( "Question 254911: Solve by substitution
\n" ); document.write( "y^2=1+2x^2
\n" ); document.write( "x^2+2y^2=22
\n" ); document.write( "my options are
\n" ); document.write( "(3,2),(3,-2), (-2,3), (-2,-3)
\n" ); document.write( "(2,3), (2,-3), (-2,3), (-2,-3)
\n" ); document.write( "(radical 7, radical 15) (-radical 7, radical 15) (radical 7,-radical 15) (- radical 7, -radical 15)
\n" ); document.write( "(radical 15, radical 7) (radical 15, -radical 7)(-radical 15,radical 7, (-radical 15,-radical 7)
\n" ); document.write( "I am not getting any of these answers \n" ); document.write( "

Algebra.Com's Answer #187202 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2%2B2y%5E2=22\"$ Start with the second equation.
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2%281%2B2x%5E2%29=22\"$ Plug in $\"y%5E2=1%2B2x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2%2B4x%5E2=22\"$ Distribute\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2%2B4x%5E2-22=0\"$ Subtract 22 from both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%5E2-20=0\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic $\"5x%5E2-20\"$ is in the form of $\"Ax%5E2%2BBx%2BC\"$ where $\"A=5\"$ , $\"B=0\"$ , and $\"C=-20\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"x\":\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"$ Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%285%29%28-20%29+%29%29%2F%282%285%29%29\"$ Plug in $\"A=5\"$ , $\"B=0\"$ , and $\"C=-20\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+sqrt%28+0-4%285%29%28-20%29+%29%29%2F%282%285%29%29\"$ Square $\"0\"$ to get $\"0\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+sqrt%28+0--400+%29%29%2F%282%285%29%29\"$ Multiply $\"4%285%29%28-20%29\"$ to get $\"-400\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+sqrt%28+0%2B400+%29%29%2F%282%285%29%29\"$ Rewrite $\"sqrt%280--400%29\"$ as $\"sqrt%280%2B400%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+sqrt%28+400+%29%29%2F%282%285%29%29\"$ Add $\"0\"$ to $\"400\"$ to get $\"400\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+sqrt%28+400+%29%29%2F%2810%29\"$ Multiply $\"2\"$ and $\"5\"$ to get $\"10\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B-+20%29%2F%2810%29\"$ Take the square root of $\"400\"$ to get $\"20\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%280+%2B+20%29%2F%2810%29\"$ or $\"x+=+%28-0+-+20%29%2F%2810%29\"$ Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%2820%29%2F%2810%29\"$ or $\"x+=++%28-20%29%2F%2810%29\"$ Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+2\"$ or $\"x+=+-2\"$ Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the solutions for 'x' are $\"x+=+2\"$ or $\"x+=+-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now take each solution for 'x' and plug them into $\"y%5E2=1%2B2x%5E2\"$ to find the corresponding 'y' solutions.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the corresponding solutions for y when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B2x%5E2\"$ Start with the first equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B2%282%29%5E2\"$ Plug in $\"x=2\"$ (the first 'x' solution)\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B2%284%29\"$ Square 2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B8\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=9\"$ Add\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%22%22%2B-sqrt%289%29\"$ Take the square root of both sides (don't forget the plus/minus)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=sqrt%289%29\"$ or $\"y=-sqrt%289%29\"$ Break up the plus/minus\r
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\n" ); document.write( "\n" ); document.write( " $\"y=3\"$ or $\"y=-3\"$ Take the square root of 9 to get 3.\r
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\n" ); document.write( "\n" ); document.write( "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)\r
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\n" ); document.write( "\n" ); document.write( "Now let's find the corresponding solutions for y when $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B2x%5E2\"$ Start with the first equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B2%282%29%5E2\"$ Plug in $\"x=-2\"$ (the second 'x' solution)\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B2%284%29\"$ Square 2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=1%2B8\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2=9\"$ Add\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%22%22%2B-sqrt%289%29\"$ Take the square root of both sides (don't forget the plus/minus)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=sqrt%289%29\"$ or $\"y=-sqrt%289%29\"$ Break up the plus/minus\r
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\n" ); document.write( "\n" ); document.write( " $\"y=3\"$ or $\"y=-3\"$ Take the square root of 9 to get 3.\r
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\n" ); document.write( "\n" ); document.write( "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)\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the four ordered pair solutions are (2,3), (2,-3), (-2,3), and (-2,-3) which means that the answer is B) \n" ); document.write( "

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