document.write( "Question 108984: Solve each of the following systems by graphing.
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Algebra.Com's Answer #79470 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Solve each of the following systems by graphing.\r\n" );
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document.write( " x - 2y =  8\r\n" );
document.write( "3x - 2y = 12\r\n" );
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document.write( "Get two points on the first line.\r\n" );
document.write( "Plot them and draw a line through them.\r\n" );
document.write( "Get two points on the second line.\r\n" );
document.write( "Plot them and draw a line through them.\r\n" );
document.write( "Identify the coodinates of the point where the two lines cross.\r\n" );
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document.write( "Get two points on the first line whose equation is  x - 2y =  8\r\n" );
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document.write( "Arbitrarily pick any convenient number to substitute\r\n" );
document.write( "for either letter.  I think I will first choose 0 to substitute\r\n" );
document.write( "for x.  I chose 0 simply because it is easy.  I could have chosen\r\n" );
document.write( "any other number, and for either letter.  So we substitute x = 0\r\n" );
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document.write( " x - 2y = 8\r\n" );
document.write( " 0 - 2y = 8\r\n" );
document.write( "    -2y = 8\r\n" );
document.write( "      y = \"8%2F%28-2%29\" \r\n" );
document.write( "      y = -4, so one point on the first line is (x, y) = (0,-4) \r\n" );
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document.write( "Now for the second point on the first line, I think I will choose 0 to substitute for y.  Again I chose 0 simply because it is easy.  I could \r\n" );
document.write( "have chosen any other number, and for either letter.  So we substitute\r\n" );
document.write( "y = 0\r\n" );
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document.write( "   x - 2y = 8\r\n" );
document.write( " x - 2(0) = 8\r\n" );
document.write( "    x - 0 = 8\r\n" );
document.write( "        x = 8, so another point on the first line is (x, y) = (8, 0)\r\n" );
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document.write( "Plot the two points (0, -4) and (8, 0):\r\n" );
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document.write( "Draw a straight line through them:\r\n" );
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document.write( "Get two points on the second line, whose equation is 3x - 2y = 12\r\n" );
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document.write( "Arbitrarily pick any convenient number to substitute\r\n" );
document.write( "for either letter.  I will again first choose 0 to substitute\r\n" );
document.write( "for x.  Again I chose 0 simply because it is easy.  I could have chosen\r\n" );
document.write( "any other number, and for either letter.  So we substitute x = 0\r\n" );
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document.write( "  3x - 2y = 12\r\n" );
document.write( "3(0) - 2y = 12\r\n" );
document.write( "      -2y = 12\r\n" );
document.write( "      y = \"12%2F%28-2%29\" \r\n" );
document.write( "      y = -6, so one point on the second line is (x, y) = (0,-6) \r\n" );
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document.write( "Now for the second point on the second line, I will again choose 0 to\r\n" );
document.write( "substitute for y.  Again I chose 0 simply because it is easy.  I could \r\n" );
document.write( "have chosen any other number, and for either letter.  So we substitute\r\n" );
document.write( "y = 0\r\n" );
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document.write( "  3x - 2y = 12\r\n" );
document.write( "3x - 2(0) = 12\r\n" );
document.write( "   3x - 0 = 12\r\n" );
document.write( "       3x = 12\r\n" );
document.write( "        x = \"12%2F3\"\r\n" );
document.write( "        x = 4\r\n" );
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document.write( "so another point on the second line is (x, y) = (4, 0)\r\n" );
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document.write( "Plot the two points (0, -6) and (4, 0):\r\n" );
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document.write( "Draw a straight line through them:\r\n" );
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document.write( "To identify the coodinates of the point where the \r\n" );
document.write( "two lines cross, draw both a horizontal line and\r\n" );
document.write( "a vertical line through that point. These are the\r\n" );
document.write( "green lines below:\r\n" );
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document.write( "Notice that the vertical green line goes through 2 on\r\n" );
document.write( "the x-axis, and the horizontal one goes through -3 on\r\n" );
document.write( "the y-axis, so the solution is \r\n" );
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document.write( "(x, y) = (2,-3)\r\n" );
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document.write( "We now check to see if we are correct. \r\n" );
document.write( "First we substitute x = 2, and y = -3 into the first\r\n" );
document.write( "equation to see if we get a true statement:\r\n" );
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document.write( "   x - 2y = 8\r\n" );
document.write( "2 - 2(-3) = 8\r\n" );
document.write( "    2 + 6 = 8\r\n" );
document.write( "        8 = 8\r\n" );
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document.write( "That is true, but to completely check the problem\r\n" );
document.write( "we must also substitute x = 2, and y = -3 into the second\r\n" );
document.write( "equation to see if we also get a true statement.\r\n" );
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document.write( "     3x - 2y = 12\r\n" );
document.write( "3(2) - 2(-3) = 8\r\n" );
document.write( "       6 + 6 = 12\r\n" );
document.write( "          12 = 12\r\n" );
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document.write( "That is true also, so (x, y) = (2, -3) is the correct\r\n" );
document.write( "solution to the system.\r\n" );
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document.write( "Edwin
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