document.write( "Question 82813: solve the system by graphing \r
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Algebra.Com's Answer #59409 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "solve the system by graphing \r\n" );
document.write( "x + y = 3\r\n" );
document.write( "x + y = -1\r\n" );
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document.write( "The idea is to graph both lines and find the\r\n" );
document.write( "point where they cross, or intersect.\r\n" );
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document.write( "Get three points on the first line:\r\n" );
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document.write( "x + y = 3\r\n" );
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document.write( "Pick an arbitrary value for x or y.\r\n" );
document.write( "I'll arbitrarily pick the value 2 \r\n" );
document.write( "and arbitrarily pick the letter x\r\n" );
document.write( "to substitute it for:\r\n" );
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document.write( "2 + y = 3\r\n" );
document.write( "    y = 3 - 2\r\n" );
document.write( "    y = 1\r\n" );
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document.write( "So (x,y) = (2,1) is one point on the first line\r\n" );
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document.write( "Next I'll arbitrarily pick the value 4 \r\n" );
document.write( "and arbitrarily pick the letter y\r\n" );
document.write( "to substitute it for:\r\n" );
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document.write( "x + 4 = 3\r\n" );
document.write( "    x = 3 - 4\r\n" );
document.write( "    x = -1\r\n" );
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document.write( "So (x,y) = (-1,4) is another point on the first line\r\n" );
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document.write( "As a check, I'll find a third point\r\n" );
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document.write( "Next I'll arbitrarily pick the value -3 \r\n" );
document.write( "and arbitrarily pick the letter y\r\n" );
document.write( "to substitute it for:\r\n" );
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document.write( "x + (-3) = 3\r\n" );
document.write( "   x - 3 = 3\r\n" );
document.write( "       x = 3 + 3\r\n" );
document.write( "       x = 6 \r\n" );
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document.write( "So (x,y) = (6,-3) is another point on the first line\r\n" );
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document.write( "Plot those points\r\n" );
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document.write( "Now I'll draw a smooth dark red straight line through them:\r\n" );
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document.write( "Now I'll do the same for the other equation:\r\n" );
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document.write( "Get three points on the second line:\r\n" );
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document.write( "x + y = -1\r\n" );
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document.write( "Pick an arbitrary value for x or y.\r\n" );
document.write( "I'll arbitrarily pick the value 3 \r\n" );
document.write( "and arbitrarily pick the letter x\r\n" );
document.write( "to substitute it for:\r\n" );
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document.write( "3 + y = -1\r\n" );
document.write( "    y = -1 - 3\r\n" );
document.write( "    y = -4\r\n" );
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document.write( "So (x,y) = (3,-4) is one point on the 2nd line\r\n" );
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document.write( "Next I'll arbitrarily pick the value 0 \r\n" );
document.write( "and arbitrarily pick the letter y\r\n" );
document.write( "to substitute it for:\r\n" );
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document.write( "x + 0 = -1\r\n" );
document.write( "    x = -1\r\n" );
document.write( "    \r\n" );
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document.write( "So (x,y) = (-1,0) is another point on the 2nd line\r\n" );
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document.write( "As a check, I'll find a third point\r\n" );
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document.write( "Next I'll arbitrarily pick the value -2 \r\n" );
document.write( "and arbitrarily pick the letter x\r\n" );
document.write( "to substitute it for:\r\n" );
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document.write( "(-2) + y = -1\r\n" );
document.write( "  -2 + y = -1\r\n" );
document.write( "       y = -1 + 2\r\n" );
document.write( "       x = 1 \r\n" );
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document.write( "So (x,y) = (1,-2) is another point on the 2nd line\r\n" );
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document.write( "Plot those points\r\n" );
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document.write( "Now draw a smooth green straight line through them:\r\n" );
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document.write( "Oh. my! It looks like the dark red line and the\r\n" );
document.write( "green line run parallel to each other, so they\r\n" );
document.write( "will never intersect. That means there is no\r\n" );
document.write( "solution.  This is called an inconsistent\r\n" );
document.write( "system of equations.\r\n" );
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document.write( "Edwin

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