document.write( "Question 57804: Solve the system of linear equations by graphing\r
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Algebra.Com's Answer #39483 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
y = x + 3\r\n" );
document.write( "3x + y = -1\r\n" );
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document.write( "Graph the first line by getting some points:\r\n" );
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document.write( "For the first line, get three points.  Choose 3\r\n" );
document.write( "arbitrary numbers for one letter, substitute them\r\n" );
document.write( "into the first equation and solve for the other\r\n" );
document.write( "letter. Them make them into a point (x,y)\r\n" );
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document.write( "Arbitrarily choose 1 to substitute for y\r\n" );
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document.write( "                   y = x + 3 \r\n" );
document.write( "                   1 = x + 3\r\n" );
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document.write( "subtract 3 from both sides\r\n" );
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document.write( "                  -2 = x\r\n" );
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document.write( "plot the point (-2,1)\r\n" );
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document.write( "Arbitrarily choose 0 to substitute for x\r\n" );
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document.write( "                   y = x + 3 \r\n" );
document.write( "                   y = 0 + 3\r\n" );
document.write( "                   y = 3\r\n" );
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document.write( "plot the point (0,3)\r\n" );
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document.write( "Arbitrarily choose 2 to substitute for x\r\n" );
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document.write( "                   y = x + 3 \r\n" );
document.write( "                   y = 2 + 3\r\n" );
document.write( "                   y = 5\r\n" );
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document.write( "plot the point (2,5)\r\n" );
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document.write( "Draw a red line through these three points:\r\n" );
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document.write( "\"+graph%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2C+x%2B3%29+\"\r\n" );
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document.write( "Likewise for the second line, get three points.\r\n" );
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document.write( "Arbitrarily choose 5 to substitute for y\r\n" );
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document.write( "                   3x + y = -1\r\n" );
document.write( "                   3x + 5 = -1\r\n" );
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document.write( "subtract 5 from both sides\r\n" );
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document.write( "                       3x = -6\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "                        x = -2\r\n" );
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document.write( "plot the point (-2,5) on the same graph.\r\n" );
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document.write( "Arbitrarily choose 0 to substitute for x\r\n" );
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document.write( "                   3x + y = -1\r\n" );
document.write( "                 3(0) + y = -1\r\n" );
document.write( "                    0 + y = -1\r\n" );
document.write( "                        y = -1\r\n" );
document.write( "plot the point (0,-1)\r\n" );
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document.write( "Arbitrarily choose 1 to substitute for x\r\n" );
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document.write( "                   3x + y = -1\r\n" );
document.write( "                 3(1) + y = -1\r\n" );
document.write( "                    3 + y = -1\r\n" );
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document.write( "subtract 3 from both sides\r\n" );
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document.write( "                        y = -4\r\n" );
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document.write( "plot the point (1,-4)\r\n" );
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document.write( "Draw a green line through these three points:\r\n" );
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document.write( "Now you have this graph:\r\n" );
document.write( "\"+graph%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2C+x%2B3%2C+-1-3x%29+\"\r\n" );
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document.write( "Notice the the red and green lines cross at the point\r\n" );
document.write( "which is directly above -1 on the x axis, and which\r\n" );
document.write( "is directly to the left of 2 on the y-axis.\r\n" );
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document.write( "Therefore the solution is (x,y) = (-1,2) which\r\n" );
document.write( "means x = -1 and y = 2\r\n" );
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document.write( "Now we check to see if the solution is correct.\r\n" );
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document.write( "We substitute both x = -1 and y = 2 into the first\r\n" );
document.write( "equation:\r\n" );
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document.write( "                   y =  x + 3 \r\n" );
document.write( "                   2 = -1 + 3\r\n" );
document.write( "                   2 = 2\r\n" );
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document.write( "So the first equation checks.  But that is not\r\n" );
document.write( "enough. We must also substitute both x = -1 and y = 2 \r\n" );
document.write( "into the second equation as well.\r\n" );
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document.write( "                    3x + y = -1\r\n" );
document.write( "                 3(-1) + 2 = -1\r\n" );
document.write( "                    -3 + 2 = -1\r\n" );
document.write( "                        -1 = -1\r\n" );
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document.write( "That equation checks also, so (-1,2) is the correct\r\n" );
document.write( "solution.\r\n" );
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document.write( "Edwin

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