document.write( "Question 653268: 2x-3y+5z=13
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Algebra.Com's Answer #408317 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "2x - 3y + 5z = 13\r\n" );
document.write( "4x + 4y + 6z = 34\r\n" );
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document.write( "Since you want the y-variable by itself, get the y-terms off the\r\n" );
document.write( "left sides and onto the right side\r\n" );
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document.write( "2x + 5z = 13 + 3y\r\n" );
document.write( "4x + 6z = 34 - 4y\r\n" );
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document.write( "Eliminate x by multiplying the first equation by -2 and adding\r\n" );
document.write( "it term-by-term to the second equation:\r\n" );
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document.write( "-4x - 10z = -26 - 6y\r\n" );
document.write( " 4x +  6z =  34 - 4y\r\n" );
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document.write( "      -4z =   8 - 10y\r\n" );
document.write( "        z =  - y\r\n" );
document.write( "        z = -2 + y \r\n" );
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document.write( "Go back to\r\n" );
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document.write( "2x + 5z = 13 + 3y\r\n" );
document.write( "4x + 6z = 34 - 4y\r\n" );
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document.write( "Eliminate z by multiplying the first equation by -6\r\n" );
document.write( "and the second equation by 5\r\n" );
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document.write( "-12x - 30z = -78 - 18y\r\n" );
document.write( " 20x + 30z = 170 - 20y\r\n" );
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document.write( "  8x       =  92 - 38y \r\n" );
document.write( "         x =  - y\r\n" );
document.write( "         x =  - y\r\n" );
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document.write( "So the solution with y by itself is\r\n" );
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document.write( "(x, y, z) = ( - y, y, -2 + y)\r\n" );
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document.write( "Edwin

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