document.write( "Question 78872: Solve each system by graphing.
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Algebra.Com's Answer #56610 by Edwin McCravy(20077) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Solve each system by graphing.\r\n" );
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document.write( "3x - 2y = 6\r\n" );
document.write( "6x + 2y = -12\r\n" );
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document.write( "Let's graph the first line by finding two points:\r\n" );
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document.write( "Let the x coordinate of the point be 0, since 0\r\n" );
document.write( "is the easiest number to substitute in any equation:\r\n" );
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document.write( "So substituting 0 for x in\r\n" );
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document.write( "  3x - 2y = 6\r\n" );
document.write( "3(0) - 2y = 6\r\n" );
document.write( "   0 - 2y = 6\r\n" );
document.write( "      -2y = 6\r\n" );
document.write( "        y = 6/(-2)\r\n" );
document.write( "        y = -3\r\n" );
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document.write( "So one point, the y-intercept is (0, -3)\r\n" );
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document.write( "Now let the y coordinate of a point be 0, since 0\r\n" );
document.write( "is the easiest number to substitute in any equation:\r\n" );
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document.write( "So substituting 0 for y in\r\n" );
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document.write( "  3x - 2y = 6\r\n" );
document.write( "3x - 2(0) = 6\r\n" );
document.write( "       3x = 6\r\n" );
document.write( "        x = 6/3\r\n" );
document.write( "        x = 2\r\n" );
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document.write( "So another point, the x-intercept, is (2, 0)\r\n" );
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document.write( "Plot those points and draw a line through them:\r\n" );
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document.write( "6x + 2y = -12\r\n" );
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document.write( "Now let's graph the second line the same way, by\r\n" );
document.write( "finding two points:\r\n" );
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document.write( "Let the x coordinate of the point be 0, since 0\r\n" );
document.write( "is the easiest number to substitute in any equation:\r\n" );
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document.write( "So substituting 0 for x in\r\n" );
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document.write( "  6x + 2y = -12\r\n" );
document.write( "6(0) + 2y = -12\r\n" );
document.write( "   0 + 2y = -12\r\n" );
document.write( "       2y = -12\r\n" );
document.write( "        y = -12/2\r\n" );
document.write( "        y = -6\r\n" );
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document.write( "So one point, the y-intercept is (0, -6)\r\n" );
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document.write( "Now let the y coordinate of a point be 0, since 0\r\n" );
document.write( "is the easiest number to substitute in any equation:\r\n" );
document.write( "\r\n" );
document.write( "So substituting 0 for y in\r\n" );
document.write( "\r\n" );
document.write( "  6x + 2y = -12\r\n" );
document.write( "6x + 2(0) = -12\r\n" );
document.write( "       6x = -12\r\n" );
document.write( "        x = -12/6\r\n" );
document.write( "        x = -2\r\n" );
document.write( "        \r\n" );
document.write( "So another point, the x-intercept, is (-2, 0)\r\n" );
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document.write( "Plot those points on the same set of axes as\r\n" );
document.write( "the first line and draw a line through them:\r\n" );
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document.write( "Now draw a horizontal line through the point where \r\n" );
document.write( "the two lines cross:\r\n" );
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document.write( "Now draw a vertical line through the point where \r\n" );
document.write( "the two lines cross:\r\n" );
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document.write( "Notice that the horizontal line crosses the y-axis at -4, so the\r\n" );
document.write( "y-coordinate of the solution is y = -4\r\n" );
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document.write( "The vertical line crosses the x-axis at a point between -1 and 0,\r\n" );
document.write( "and we can estimate that to be about 2/3 of the way from 0 to -1,\r\n" );
document.write( "so that would make the x-coordinate of the solution be x = -2/3.\r\n" );
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document.write( "Now we check to see if we have the correct answer, by substituting\r\n" );
document.write( "in both original equations:\r\n" );
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document.write( "Substituting (x,y) = (-2/3,-4) in the first equation\r\n" );
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document.write( "        3x - 2y = 6\r\n" );
document.write( "3(-2/3) - 2(-4) = 6\r\n" );
document.write( "       -6/3 + 8 = 6\r\n" );
document.write( "         -2 + 8 = 6\r\n" );
document.write( "              6 = 6\r\n" );
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document.write( "That checks. \r\n" );
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document.write( "6x + 2y = -12\r\n" );
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document.write( "Substituting (x,y) = (-2/3,-4) in the second equation\r\n" );
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document.write( "        6x + 2y = -12\r\n" );
document.write( "6(-2/3) + 2(-4) = -12\r\n" );
document.write( "      -12/3 - 8 = -12\r\n" );
document.write( "         -4 - 8 = -12\r\n" );
document.write( "            -12 = -12\r\n" );
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document.write( "That checks, too.  So the solution\r\n" );
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document.write( "(x,y) = (-2/3,-4)\r\n" );
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document.write( "is correct.\r\n" );
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document.write( "Edwin
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