document.write( "Question 131468: For the following systems of linear equations:
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Algebra.Com's Answer #96044 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
For the following systems of linear equations:
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document.write( "5x + 6y = 1 and x + 7y = 2 \r\n" );
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document.write( "Let's use elimination:\r\n" );
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document.write( "5x + 6y = 1  \r\n" );
document.write( " x + 7y = 2\r\n" );
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document.write( "Multiply the bottom equation by -5 to eliminate the x's\r\n" );
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document.write( " 5x +  6y =   1  \r\n" );
document.write( "-5x - 35y = -10\r\n" );
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document.write( "     -29y =  -9\r\n" );
document.write( "        y = \"%28-9%29%2F%28-29%29\"\r\n" );
document.write( "        y = \"9%2F29\"\r\n" );
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document.write( "Since the answer is complicated, start over\r\n" );
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document.write( "5x + 6y = 1  \r\n" );
document.write( " x + 7y = 2\r\n" );
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document.write( "This time eliminate the y's by multiplying the \r\n" );
document.write( "first equation through by -7 and the second one \r\n" );
document.write( "through by +6:\r\n" );
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document.write( "-35x - 42y = -7  \r\n" );
document.write( "  6x + 42y = 12\r\n" );
document.write( "---------------\r\n" );
document.write( "-29x       =  5\r\n" );
document.write( "   x       = \"5%2F%28-29%29\"\r\n" );
document.write( "         x = \"-5%2F29\"\r\n" );
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document.write( "c) Graph the two lines, labeling the x-intercepts, \r\n" );
document.write( "y-intercepts and points of intersection. \r\n" );
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document.write( "Find the x-intercept by substituting 0 for y and\r\n" );
document.write( "solving for x\r\n" );
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document.write( "  5x + 6y = 1\r\n" );
document.write( "5x + 6(0) = 1\r\n" );
document.write( "   5x + 0 = 1\r\n" );
document.write( "       5x = 1\r\n" );
document.write( "        x = \"1%2F5\"\r\n" );
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document.write( "So the x-intercept is the point (\"1%2F5\",0)\r\n" );
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document.write( "Find the y-intercept by substituting 0 for x and\r\n" );
document.write( "solving for y\r\n" );
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document.write( "  5x + 6y = 1\r\n" );
document.write( "5(0) + 6y = 1\r\n" );
document.write( "   0 + 6y = 1\r\n" );
document.write( "       6y = 1\r\n" );
document.write( "        y = \"1%2F6\"\r\n" );
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document.write( "So the y-intercept is the point (0,\"1%2F6\")\r\n" );
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document.write( "Get some points on the first line:\r\n" );
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document.write( "(-7,6), (-1,1), (5,-4)\r\n" );
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document.write( "Plot them and draw a line through them:\r\n" );
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document.write( "The x- and y-intercepts are so close together and\r\n" );
document.write( "so close to the origin it is impossible to label\r\n" );
document.write( "them on this graph.  We'll zoom in on it later.\r\n" );
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document.write( "Now let's draw the second line:\r\n" );
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document.write( "Find the x-intercept by substituting 0 for y and\r\n" );
document.write( "solving for x\r\n" );
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document.write( "  x + 7y = 2\r\n" );
document.write( "x + 7(0) = 2\r\n" );
document.write( "   x + 0 = 2\r\n" );
document.write( "       x = 2\r\n" );
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document.write( "So the x-intercept is the point (2,0)\r\n" );
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document.write( "Find the y-intercept by substituting 0 for x and\r\n" );
document.write( "solving for y\r\n" );
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document.write( "   x + 7y = 2\r\n" );
document.write( " (0) + 7y = 2\r\n" );
document.write( "       7y = 2\r\n" );
document.write( "        y = \"2%2F7\"\r\n" );
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document.write( "So the y-intercept is the point (0,\"2%2F7\")\r\n" );
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document.write( "Get some points on the second line:\r\n" );
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document.write( "(-5,1), (2,0), (9,-1)\r\n" );
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document.write( "Plot them and draw a line through them:\r\n" );
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document.write( "Now we put them both on the same graph\r\n" );
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document.write( "It's too hard to label everything on\r\n" );
document.write( "that graph, because all those points are\r\n" );
document.write( "scrunched up together near the origin, \r\n" );
document.write( "so let's zoom in on a small section of\r\n" );
document.write( "the graph:\r\n" );
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document.write( "point A is the x-intercept of the first line, (\"1%2F5\",0)\r\n" );
document.write( "point B is the y-intercept of the first line, (0,\"1%2F6\")\r\n" );
document.write( "point C is the x-intercept of the second line, (2,0)\r\n" );
document.write( "point D is the y-intercept of the scond line, (0,\"2%2F7\")\r\n" );
document.write( "point E is their point of intersection, (\"-5%2F29\",\"9%2F29\")\r\n" );
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document.write( "Edwin
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