document.write( "Question 1053721: 4x^2 + 9y^2 = 72
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\n" ); document.write( "\n" ); document.write( "Select all of the following that are solutions to the system shown.
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Algebra.Com's Answer #668936 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "4x^2 + 9y^2 = 72
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\n" ); document.write( "\n" ); document.write( "Select all of the following that are solutions to the system shown.
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document.write( "4x^2 + 9y^2 = 72,   (1)\r\n" );
document.write( "x - y^2 = -1.       (2)\r\n" );
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document.write( "To solve it algebraically, express y^2 = x+1 from the equation (2) and substitute it into equation (1). You will get\r\n" );
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document.write( "4x^2 + 9(x+1) = 72.\r\n" );
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document.write( "In this way you got a single equation for only one unknown x.\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "4x^2 + 9x - 63 = 0,\r\n" );
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document.write( " =  = .\r\n" );
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document.write( " =  = 3,   =  = -5.25.\r\n" );
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document.write( "The negative root doesn't suit the equation y^2 = x+1, since the right site would be negative.\r\n" );
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document.write( "So, the only solution for x is x=3.\r\n" );
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document.write( "Then you get two solutions for y: y^2 = x+1 = 3+1 = 4 and   = 2,   = -2.\r\n" );
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document.write( "Answer. The system has two solutions (x,y) = (3,2)  and  (x,y) = (3,-2).\r\n" );
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\n" ); document.write( "\n" ); document.write( "For many other solved similar problems see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of algebraic equations of degree 2 and degree 1 \r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of algebraic equations of degree 2 \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of equations that are not linear\".\r
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