document.write( "Question 67343: Hi, can someone please help me solve the following by graphing? Thanks in advance!\r
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\n" ); document.write( "\n" ); document.write( "1. 3x - 5y = -9
\n" ); document.write( " 5x - 6y = -8\r
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\n" ); document.write( "\n" ); document.write( "2. 4x + 5y = -2
\n" ); document.write( " 4y - x = 11\r
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Algebra.Com's Answer #47903 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Hi, can someone please help me solve the following by \r\n" );
document.write( "graphing? Thanks in advance! \r\n" );
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document.write( "1. 3x - 5y = -9\r\n" );
document.write( "   5x - 6y = -8\r\n" );
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document.write( "Get some points on the first line:\r\n" );
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document.write( "(-8,-3), (-3,0), and (7,6), plot them and draw\r\n" );
document.write( "a red line through them:\r\n" );
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document.write( " \"+graph%28+350%2C+350%2C+-10%2C+10%2C+-10%2C+10%2C+%28-9-3x%29%2F%28-5%29%29+\"\r\n" );
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document.write( "Get some points on the second line:\r\n" );
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document.write( "(-10,-7), (-4,-2), and (8,8), plot them and draw\r\n" );
document.write( "a green line through them:\r\n" );
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document.write( "Now we have to guess where the two lines intersect. To do this\r\n" );
document.write( "draw a blue vertical line through the point of intersection: \r\n" );
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document.write( "Notice that it crosses the x-axis at 2, so the x coordinate of the\r\n" );
document.write( "point of intersection is 2.\r\n" );
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document.write( "Now draw a horizontal line through the point of intersection: \r\n" );
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document.write( "Notice that it crosses the y-axis at 3, so the y coordinate of the\r\n" );
document.write( "point of intersection is 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( "Check substitute 2 for x and 3 for y in both original equations:\r\n" );
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document.write( "   3x - 5y = -9\r\n" );
document.write( "   5x - 6y = -8\r\n" );
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document.write( "   3(2) - 5(3) = -9\r\n" );
document.write( "   5(2) - 6(3) = -8\r\n" );
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document.write( "     6 - 15 = -9\r\n" );
document.write( "    10 - 18 = -8\r\n" );
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document.write( "         -9 = -9\r\n" );
document.write( "         -8 = -8\r\n" );
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document.write( "It checks.\r\n" );
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document.write( "2. 4x + 5y = -2\r\n" );
document.write( "   4y -  x = 11 \r\n" );
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document.write( "Get some points on the first line:\r\n" );
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document.write( "(-8,6), (2,-2), and (7,-6), plot them and draw\r\n" );
document.write( "a red line through them:\r\n" );
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document.write( " \"+graph%28+350%2C+350%2C+-10%2C+10%2C+-10%2C+10%2C+%28-2-4x%29%2F5%29+\"\r\n" );
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document.write( "Get some points on the second line:\r\n" );
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document.write( "(-7,1), (5,4), and (9,5), plot them and draw\r\n" );
document.write( "a green line through them:\r\n" );
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document.write( " \"+graph%28+350%2C+350%2C+-10%2C+10%2C+-10%2C+10%2C+%28-2-4x%29%2F5%2C+%2811%2Bx%29%2F4%29+\"\r\n" );
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document.write( "Now we have to guess where the two lines intersect. To do this\r\n" );
document.write( "draw a blue vertical line through the point of intersection: \r\n" );
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document.write( " \r\n" );
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document.write( "Notice that it crosses the x-axis at -3, so the x coordinate of the\r\n" );
document.write( "point of intersection is -3.\r\n" );
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document.write( "Now draw a horizontal line through the point of intersection: \r\n" );
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document.write( "Notice that it crosses the y-axis at 2, so the y coordinate of the\r\n" );
document.write( "point of intersection is 2.\r\n" );
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document.write( "So the solution is (x,y) = (-3,2)\r\n" );
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document.write( "Check substitute -3 for x and 2 for y in both original equations:\r\n" );
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document.write( "2. 4x + 5y = -2\r\n" );
document.write( "   4y -  x = 11\r\n" );
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document.write( "   4(-3) + 5(2) = -2\r\n" );
document.write( "    4(2) - (-3) = 11\r\n" );
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document.write( "   -12 + 10 = -2\r\n" );
document.write( "     8 +  3 = 11\r\n" );
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document.write( "         -2 = -2\r\n" );
document.write( "         11 = 11\r\n" );
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document.write( "It checks.\r\n" );
document.write( "Edwin
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