document.write( "Question 1099296: I have this problem (the two equations should be in brackets with each other because they can be used to solve for each other): $\"x%5E2%2By%5E2=4\"$ and $\"3x-y=2\"$ . I got two answers (0,2) and (6/5,8/5). Only the later answer solved completely. Does that mean it is the only real answer, or does this mean I got both answers wrong? Thanks for helping! \n" ); document.write( "

Algebra.Com's Answer #713745 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "First of all, by substituting your \"solutions\" directly into the given equations (\"the \"CHECKING\" step) \r
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\n" ); document.write( "\n" ); document.write( "you can see that (0,2) IS NOT THE SOLUTION, while (6/5,8/5) IS.\r
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document.write( "Let solve this system together:\r\n" );
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document.write( " = 4,     (1)\r\n" );
document.write( "3x - y = 2.     (2)\r\n" );
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document.write( "From (2), express y = 3x-2. Next, substitute it into equation (1), replacing \"y\". You will get \r\n" );
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document.write( " = 4.\r\n" );
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document.write( "Simplify it step by step:\r\n" );
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document.write( " = 4  ====>   = 0  ====>  (factoring left side)  ====>\r\n" );
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document.write( "2x*(5x-6) = 0.\r\n" );
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document.write( "The solutions for x are  0  and   x= .\r\n" );
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document.write( "a)  If  x= 0,  then  from (2)  y = 3x-2 = 3*0-2 = -2.\r\n" );
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document.write( "    So, the pair  (x,y) = (0,-2)  is one solution.\r\n" );
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document.write( "b)  If x= ,  then  y = 3x-2 =  =  = .\r\n" );
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document.write( "     So, the pair  (x,y) = (6/5,8/5) is the other solution.\r\n" );
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document.write( "Answer.  The solutions are  (0,-2)  and  (6/5,8/5).\r\n" );
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\n" ); document.write( "\n" ); document.write( "You can CHECK that these pairs satisfy both original equations.\r
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\n" ); document.write( "\n" ); document.write( "---------------
\n" ); document.write( "To see more solved problems for systems of equations of this type, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving the system of algebraic equations of degree 2 and degree 1, \r
\n" ); document.write( "\n" ); document.write( "    - Solving the system 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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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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