document.write( "Question 329392: Show me how to use elimination to solve the system of equations given by
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Algebra.Com's Answer #236066 by Edwin McCravy(20062) $\"\"$ $\"About$

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Show me how to use elimination to solve the system of equations given by
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document.write( "Draw a line underneath:\r\n" );
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document.write( "3x-2y=10 \r\n" );
document.write( "5x+2y= 6\r\n" );
document.write( "--------\r\n" );
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document.write( "Add the red 3x to the red 5x.  That gives 8x.  Write that down below the line.\r\n" );
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document.write( "3x-2y=10 \r\n" );
document.write( "5x+2y= 6\r\n" );
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document.write( "8x\r\n" );
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document.write( "Add the green -2y to the green +2y.  But they just cancel out because they are\r\n" );
document.write( "just alike except one has a - before it and the other has a +\r\n" );
document.write( "before it:\r\n" );
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document.write( "3x-2y=10 \r\n" );
document.write( "5x+2y= 6\r\n" );
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document.write( "8x\r\n" );
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document.write( "Next bring down the equal sign\r\n" );
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document.write( "3x-2y=10 \r\n" );
document.write( "5x+2y= 6\r\n" );
document.write( "--------\r\n" );
document.write( "8x   =\r\n" );
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document.write( "Now add the 10 and the 6 getting 16. Write that down:\r\n" );
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document.write( "3x-2y=10 \r\n" );
document.write( "5x+2y= 6\r\n" );
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document.write( "8x   =16\r\n" );
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document.write( "Now you have the equation\r\n" );
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document.write( "Divide both sides by 8:\r\n" );
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document.write( "x = 2\r\n" );
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document.write( "Go back to one of the original equations:\r\n" );
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document.write( "3x-2y=10\r\n" );
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document.write( "In place of x, substitute (2)\r\n" );
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document.write( "3(2)-2y=10\r\n" );
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document.write( "Multiply the 3 by the 2 getting 6\r\n" );
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document.write( "   6-2y=10\r\n" );
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document.write( "Add -6 to both sides:\r\n" );
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document.write( "   6-2y=10\r\n" );
document.write( "  -6    -6\r\n" );
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document.write( "    -2y= 4\r\n" );
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document.write( "Now we have the equation:\r\n" );
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document.write( "We divide both sides by -2\r\n" );
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document.write( "y = -2\r\n" );
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document.write( "So the solution is (x,y) = (2,-2)\r\n" );
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document.write( "To check we substitute (2) for x and (-2) for y in each equation\r\n" );
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document.write( "     3x-2y=10 and      5x+2y=6\r\n" );
document.write( "3(2)-2(-2)=10 and 5(2)+2(-2)=6\r\n" );
document.write( "       6+4=10 and       10-4=6\r\n" );
document.write( "        10=10 and          6=6\r\n" );
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document.write( "So the solution is correct.\r\n" );
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document.write( "Edwin

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