document.write( "Question 79725: 3x-2y=8
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Algebra.Com's Answer #57204 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "solve the following system of equations by graphing\r\n" );
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document.write( "3x - 2y = 8\r\n" );
document.write( "2x - 3y = 7 \r\n" );
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document.write( "Make a table of points for each equationm:\r\n" );
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document.write( "In the first, I arbitrarily chooss -2 for x\r\n" );
document.write( "and substitute:\r\n" );
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document.write( "   3x - 2y = 8\r\n" );
document.write( "3(-2) - 2y = 8\r\n" );
document.write( "   -6 - 2y = 8\r\n" );
document.write( "       -2y = 14\r\n" );
document.write( "         y = -7\r\n" );
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document.write( "So one point on the graph of the first equation\r\n" );
document.write( "in (-2,-7)\r\n" );
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document.write( "I arbitrarily chooss 2 for y\r\n" );
document.write( "and substitute:\r\n" );
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document.write( "   3x - 2y = 8\r\n" );
document.write( " 3x - 2(2) = 8\r\n" );
document.write( "    3x - 4 = 8\r\n" );
document.write( "        3x = 12\r\n" );
document.write( "         x = 4\r\n" );
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document.write( "So another point on the graph of the first equation\r\n" );
document.write( "in (4,2)\r\n" );
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document.write( "I arbitrarily chooss 0 for x\r\n" );
document.write( "and substitute:\r\n" );
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document.write( "   3x - 2y = 8\r\n" );
document.write( " 3(0) - 2y = 8\r\n" );
document.write( "    0 - 2y = 8\r\n" );
document.write( "       -2x = 8\r\n" );
document.write( "         x = -4\r\n" );
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document.write( "So a third point on the graph of the first equation\r\n" );
document.write( "in (0,-4).\r\n" );
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document.write( "So plot those points, (-2,-7), (4,2), (0,-4)\r\n" );
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document.write( "and draw a line through them:\r\n" );
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document.write( "In the second equation, I arbitrarily chooss\r\n" );
document.write( "-1 for x and substitute:\r\n" );
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document.write( "   2x - 3y = 7\r\n" );
document.write( "2(-1) - 3y = 7\r\n" );
document.write( "   -2 - 3y = 7\r\n" );
document.write( "       -3y = 9\r\n" );
document.write( "         y = -3\r\n" );
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document.write( "So one point on the graph of the second equation\r\n" );
document.write( "in (-1,-3)\r\n" );
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document.write( "I arbitrarily chooss 1 for y\r\n" );
document.write( "and substitute:\r\n" );
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document.write( "   2x - 3y = 7\r\n" );
document.write( " 2x - 3(1) = 7\r\n" );
document.write( "    2x - 3 = 7\r\n" );
document.write( "        2x = 10\r\n" );
document.write( "         x = 5\r\n" );
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document.write( "So another point on the graph of the second equation\r\n" );
document.write( "in (5,1)\r\n" );
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document.write( "I arbitrarily chooss -4 for x\r\n" );
document.write( "and substitute:\r\n" );
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document.write( "   2x - 3y = 7\r\n" );
document.write( "2(-4) - 3y = 7\r\n" );
document.write( "   -8 - 3y = 7\r\n" );
document.write( "       -3x = 15\r\n" );
document.write( "         x = -5\r\n" );
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document.write( "So a third point on the graph of the second equation\r\n" );
document.write( "in (-4,-5).\r\n" );
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document.write( "So plot those points, (-1,-3), (5,1), (-4,-5)\r\n" );
document.write( "on the same set of axes and draw a line through them:\r\n" );
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document.write( "Through the point where those two lines cross, draw\r\n" );
document.write( "a vertical line:\r\n" );
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document.write( "Notice that the vertical line crosses the x-axis at\r\n" );
document.write( "the value 2.  So the x value of the solution is 2.\r\n" );
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document.write( "Also through the point where those two lines cross, draw\r\n" );
document.write( "a horizontal line:\r\n" );
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document.write( "Notice that the horizontal line crosses the y-axis at\r\n" );
document.write( "the value -1.  So the y value of the solution is -1.\r\n" );
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document.write( "The solution is therefore (x, y) = (2, -1)\r\n" );
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document.write( "Now let's check to see if this is the correct solution\r\n" );
document.write( "by substituting in BOTH equations:\r\n" );
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document.write( "Substituting in the first:\r\n" );
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document.write( "     3x - 2y = 8\r\n" );
document.write( "3(2) - 2(-1) = 8\r\n" );
document.write( "       6 + 2 = 8\r\n" );
document.write( "           8 = 8\r\n" );
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document.write( "That checks:\r\n" );
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document.write( "Substituting in the second:\r\n" );
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document.write( "     2x - 3y = 7\r\n" );
document.write( "2(2) - 3(-1) = 7\r\n" );
document.write( "       4 + 3 = 7\r\n" );
document.write( "           7 = 7\r\n" );
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document.write( "That checks, too. So \r\n" );
document.write( "we know that this is the\r\n" );
document.write( "correct solution.\r\n" );
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document.write( "Edwin
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