document.write( "Question 39082: SPlease solve by graphing. Indicate whether each system is independent, inconsistent, or dependent. Thank you for your help\r
\n" ); document.write( "\n" ); document.write( "1. y = 3x - 4
\n" ); document.write( " y= -2x + 1\r
\n" ); document.write( "\n" ); document.write( "2. 2x - 3y = 12
\n" ); document.write( " 3y - 2x = -12 \n" ); document.write( "

Algebra.Com's Answer #24802 by AnlytcPhil(1807) $\"\"$ $\"About$

You can put this solution on YOUR website!

Please solve by graphing. Indicate whether each system is independent,\r\n" );
document.write( "inconsistent, or dependent. Thank you for your help \r\n" );
document.write( "1. y = 3x - 4 \r\n" );
document.write( "   y = -2x + 1 \r\n" );
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document.write( "2. 2x - 3y = 12\r\n" );
document.write( "   3y - 2x = -12\r\n" );
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document.write( "They are independent if their graphs (which are straight lines) intersect in a\r\n" );
document.write( "point, and the two coordinates of that point of intersection will represent the\r\n" );
document.write( "solution to that system.\r\n" );
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document.write( "They are inconsistent if their graphs (straight lines) are parallel, which\r\n" );
document.write( "means they don't intersect and therefore there can have no solution.\r\n" );
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document.write( "They are dependent if they coincide \r\n" );
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document.write( "1.\r\n" );
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document.write( "y =  3x - 4 \r\n" );
document.write( "y = -2x + 1\r\n" );
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document.write( "Get a few points on each \r\n" );
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document.write( "For y = 3x - 4 plot (-1, 7), (0, -4), (2, 2)\r\n" );
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document.write( "For y = -2x + 1 plot (-1, 3), (0, 1), (2, -3)\r\n" );
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document.write( "Draw the two lines:\r\n" );
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document.write( "The look like they cross at the point (x, y) = (1, -1)\r\n" );
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document.write( "So they are independent\r\n" );
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document.write( "====================================\r\n" );
document.write( "2.\r\n" );
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document.write( "2x - 3y = 12\r\n" );
document.write( "3y - 2x = -12\r\n" );
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document.write( "Get a few points on each \r\n" );
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document.write( "For 2x - 3y = 12 plot (0, -4), (3, -2), (6, 0)\r\n" );
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document.write( "For 3y - 2x = -12 plot (-3, -6), (-6, -8), (9, 2)\r\n" );
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document.write( "Draw the two lines:\r\n" );
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document.write( "You only see one line. That's because they coincide,\r\n" );
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document.write( "So the system of equations is dependent.  There are infinitely many solutions\r\n" );
document.write( "because every point on them represents a solution.\r\n" );
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document.write( "3.\r\n" );
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document.write( "You didn't have a system that turned out to be inconsistent.  Here's one:\r\n" );
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document.write( "2x - y = 4\r\n" );
document.write( "2y - 4x = 6\r\n" );
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document.write( "Get a few points on each \r\n" );
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document.write( "For 2x - y = 4 plot (0, -4), (2, 0), (4, 4)\r\n" );
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document.write( "For 2y - 4x = 6 plot (-1, 1), (-3, -3), (0, 3)\r\n" );
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document.write( "Draw the two lines:\r\n" );
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document.write( "They are parallel,  so they are inconsistent and have no\r\n" );
document.write( "solution.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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