document.write( "Question 728205: Solve the system of equations by graphing. Check your solution
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Algebra.Com's Answer #445355 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "2x+y = -8\r\n" );
document.write( "5x-y = -6\r\n" );
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document.write( "We get some points on each.\r\n" );
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document.write( "To get some points on \r\n" );
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document.write( "2x+y = -8\r\n" );
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document.write( "We arbitrarily choose x=0\r\n" );
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document.write( "  2x+y = -8\r\n" );
document.write( "2(0)+y = -8\r\n" );
document.write( "   0+y = -8\r\n" );
document.write( "     y = -8\r\n" );
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document.write( "So one point is (0,-8)\r\n" );
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document.write( "We arbitrarily choose y=0\r\n" );
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document.write( "  2x+y = -8\r\n" );
document.write( "  2x+0 = -8\r\n" );
document.write( "    2x = -8\r\n" );
document.write( "     x = -4\r\n" );
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document.write( "So one point is (-4,0)\r\n" );
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document.write( "We arbitrarily choose y=6\r\n" );
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document.write( "  2x+y = -8\r\n" );
document.write( "  2x+6 = -8\r\n" );
document.write( "    2x = -14\r\n" );
document.write( "     x = -7\r\n" );
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document.write( "So one point is (-7,6)\r\n" );
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document.write( "Let's plot those three points:\r\n" );
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document.write( "To get some points on \r\n" );
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document.write( "5x-y = -6\r\n" );
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document.write( "We arbitrarily choose x=0\r\n" );
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document.write( "  5x-y = -6\r\n" );
document.write( "5(0)-y = -6\r\n" );
document.write( "   0-y = -6\r\n" );
document.write( "    -y = -6\r\n" );
document.write( "     y = 6\r\n" );
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document.write( "So one point is (0,6)\r\n" );
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document.write( "We arbitrarily choose y=1\r\n" );
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document.write( "  5x-y = -6\r\n" );
document.write( "  5x-1 = -6\r\n" );
document.write( "    5x = -5\r\n" );
document.write( "     x = -1\r\n" );
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document.write( "So one point is (-1,1)\r\n" );
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document.write( "We arbitrarily choose x=-3\r\n" );
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document.write( "   5x-y = -6\r\n" );
document.write( "5(-3)-y = -6\r\n" );
document.write( "  -15-y = -6\r\n" );
document.write( "     -y =  9\r\n" );
document.write( "      y = -9\r\n" );
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document.write( "So one point is (-3,-9)\r\n" );
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document.write( "Let's plot those three points:\r\n" );
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document.write( "Now from the point where they cross, we draw one line straight to the\r\n" );
document.write( "x-axis, and another line straight to the y-axis:\r\n" );
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document.write( "We see that one blue line ends up at -2 on the x-axis, and the other\r\n" );
document.write( "blue line ends up at -4 on the y-axis, which means the solution is\r\n" );
document.write( "x=-2 and y=-4.  The point where the green and red line intersect is\r\n" );
document.write( "the point (-2,-4).\r\n" );
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document.write( "Now we check to see if when we substitute -2 for x and -4 for y in\r\n" );
document.write( "each we come out with a true equation.\r\n" );
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document.write( "Substituting them in\r\n" );
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document.write( "      2x+y = -8\r\n" );
document.write( "2(-2)+(-4) = -8\r\n" );
document.write( "      -4-4 = -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 them in\r\n" );
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document.write( "      5x-y = -6\r\n" );
document.write( "5(-2)-(-4) = -6\r\n" );
document.write( "     -10+4 = -6\r\n" );
document.write( "        -6 = -6\r\n" );
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document.write( "That also checks.  So we know that the solution is\r\n" );
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document.write( "(x,y) = (-2,-4)\r\n" );
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document.write( "Edwin
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