document.write( "Question 1171036: Solve by elimination\r
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Algebra.Com's Answer #795922 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Let me present you simple and short solution, expressed in clear human language.\r
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document.write( "Your starting equations are\r\n" );
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document.write( "    x + 3y = -13       (1)\r\n" );
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document.write( "    2x = 3y + 10       (2)\r\n" );
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document.write( "Keep the first equation as is.\r\n" );
document.write( "In the second equation, move the term 3y from the right side to the left side, changing its sign.  You will get\r\n" );
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document.write( "     x + 3y = -13      (3)\r\n" );
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document.write( "    2x - 3y =  10      (4)\r\n" );
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document.write( "    +-----------------------------------------------------------+\r\n" );
document.write( "    |   Now the system of equations is in its standard form,    |\r\n" );
document.write( "    |   and we can apply the Elimination method.                |\r\n" );
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document.write( "For it, add equations (3) and (4).  The terms \"3y\" and \"-3y\" will cancel each other, and you will get the final equation\r\n" );
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document.write( "    3x       = -3\r\n" );
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document.write( "for one single unknown x.  (It is how the elimination method works).\r\n" );
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document.write( "From this last equation,  x = -3/3 = -1.\r\n" );
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document.write( "Now substitute the found value x= -1 into either of original equations to get y.\r\n" );
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document.write( "I will substitute it into equation (1)\r\n" );
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document.write( "    -1 + 3y = -13\r\n" );
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document.write( "which gives\r\n" );
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document.write( "         3y = -13 + 1 = -12,\r\n" );
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document.write( "and then  y = -12/3 = -4.\r\n" );
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document.write( "The problem is just solved.  The  ANSWER  is  x= -1,  y= -4.\r\n" );
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document.write( "You may check the answer by substituting the found values into the original equations.\r\n" );
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document.write( "    - Did I say   \". . . you may ?\"  - - -  No, I mean  \" you MUST \".\r\n" );
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document.write( "I leave this check to you.\r\n" );
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