document.write( "Question 697656: how do I solve this system of equations by substitution\r
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Algebra.Com's Answer #430192 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( " 5x + 6y = 32\r\n" );
document.write( "12y - 4x =  8\r\n" );
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document.write( "Solve the second equation for x\r\n" );
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document.write( "12y - 4x = 8\r\n" );
document.write( "     -4x = 8 - 12y\r\n" );
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document.write( "Divide every term by the coefficient of x, which is -4:\r\n" );
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document.write( "      =  - \r\n" );
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document.write( "       x = -2 - (-3y)\r\n" );
document.write( "       x = -2 + 3y\r\n" );
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document.write( "Now substitute (-2 + 3y) for x in the other equation at\r\n" );
document.write( "the top:\r\n" );
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document.write( "        5x + 6y = 32\r\n" );
document.write( "5(-2 + 3y) + 6y = 32\r\n" );
document.write( " -10 + 15y + 6y = 32\r\n" );
document.write( "      -10 + 21y = 32\r\n" );
document.write( "            21y = 42\r\n" );
document.write( "             = \r\n" );
document.write( "              y = 2\r\n" );
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document.write( "Now go back to where you solved for x:\r\n" );
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document.write( "       x = -2 + 3y\r\n" );
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document.write( "and replace y by (2)\r\n" );
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document.write( "       x = -2 + 3(2)\r\n" );
document.write( "       x = -2 + 6\r\n" );
document.write( "       x = 4\r\n" );
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document.write( "So the solution is (x,y) = (4,2)\r\n" );
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document.write( "Checking the answer in the first equation:\r\n" );
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document.write( "     5x + 6y = 32\r\n" );
document.write( " 5(4) + 6(2) = 32\r\n" );
document.write( "     20 + 12 = 32\r\n" );
document.write( "          32 = 32\r\n" );
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document.write( "Checking the answer in the second equation:\r\n" );
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document.write( "    12y - 4x = 8\r\n" );
document.write( "12(2) - 4(4) = 8\r\n" );
document.write( "     24 - 16 = 8\r\n" );
document.write( "           8 = 8\r\n" );
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document.write( "So (x,y) = (4,2) is correct because it checks in\r\n" );
document.write( "BOTH equations.\r\n" );
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document.write( "Edwin

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