document.write( "Question 76477: Solve the system by graphing.
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Algebra.Com's Answer #54856 by Edwin McCravy(20054) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Solve the system by graphing.\r\n" );
document.write( "x - 2y = 8\r\n" );
document.write( "x + y = -1\r\n" );
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document.write( "Let's graph the first one by finding a couple of points:\r\n" );
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document.write( "Arbitrarily pick a letter, say y, and arbitrarily pick a\r\n" );
document.write( "number to substitute for it, say, -1. So\r\n" );
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document.write( "   x - 2y = 8 becomes\r\n" );
document.write( "x - 2(-1) = 8\r\n" );
document.write( "    x + 2 = 8\r\n" );
document.write( "        x = 6\r\n" );
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document.write( "So we have the point (x,y) = (6,-1)\r\n" );
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document.write( "Now arbitrarily pick a letter, say x, and arbitrarily pick\r\n" );
document.write( "another number to substitute for it, say, 4. So\r\n" );
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document.write( "   x - 2y = 8 becomes\r\n" );
document.write( "   4 - 2y = 8\r\n" );
document.write( "      -2y = 4\r\n" );
document.write( "        y = -2\r\n" );
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document.write( "So we have the point (x,y) = (4,-2)\r\n" );
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document.write( "Now we can graph the first line by plotting those two points \r\n" );
document.write( "and drawing a line through them:\r\n" );
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document.write( "Now let's graph the second one by finding a couple of points:\r\n" );
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document.write( "Arbitrarily pick a letter, say x, and arbitrarily pick a\r\n" );
document.write( "number to substitute for it, say, 0. So\r\n" );
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document.write( "   x + y = -1 becomes\r\n" );
document.write( "   0 + y = -1\r\n" );
document.write( "       y = -1\r\n" );
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document.write( "So we have the point (x,y) = (0,-1)\r\n" );
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document.write( "Now arbitrarily pick a letter, say x, and arbitrarily pick\r\n" );
document.write( "another number to substitute for it, say, 4. So\r\n" );
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document.write( "   x + y = -1 becomes\r\n" );
document.write( "   4 + y = -1\r\n" );
document.write( "       y = -5\r\n" );
document.write( "      \r\n" );
document.write( "So we have the point (x,y) = (4,-5)\r\n" );
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document.write( "Now we can graph the second line by plotting those two points \r\n" );
document.write( "and drawing a line through them:\r\n" );
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document.write( "The object is to find the coordinates of the point where they\r\n" );
document.write( "cross.  Let's draw both a horizontal line and a vertical line\r\n" );
document.write( "through the point where they cross:\r\n" );
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document.write( "Notice that the vertical line cuts the x-axis at 2 and that the\r\n" );
document.write( "horizontal line cuts the y-axis at -3.\r\n" );
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document.write( "So the solution is (x,y) = (2,-3)\r\n" );
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document.write( "Now let's check to see if we are correct by substituting 2 for\r\n" );
document.write( "x and -3 for y in both equations:\r\n" );
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document.write( "Substituting in the first:\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 checks.\r\n" );
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document.write( "Substituting in the second:\r\n" );
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document.write( "    x + y = -1\r\n" );
document.write( " 2 + (-3) = -1\r\n" );
document.write( "    2 - 3 = -1\r\n" );
document.write( "       -1 = -1\r\n" );
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document.write( "That checks.  So we know the solution is\r\n" );
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document.write( "(x,y) = (2,-3) or x = 2 and y = -3\r\n" );
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document.write( "Edwin
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