document.write( "Question 1180819: Find the constant m for which all three lines x - y = -m …eq. 1 , 2x + y = m - 1 …eq. 2, and x + 5y = 4m + 1 …eq. 3 intersect at one point. \r
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Algebra.Com's Answer #810611 by ikleyn(52795) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Find the constant m for which all three lines x - y = -m …eq. 1 , 2x + y = m - 1 …eq. 2, and x + 5y = 4m + 1 …eq. 3 intersect at one point.
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document.write( "You have these three starting equations\r\n" );
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document.write( "     x - y = -m        (1)\r\n" );
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document.write( "    2x + y =  m - 1    (2)\r\n" );
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document.write( "    x + 5y = 4m + 1    (3)\r\n" );
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document.write( "Add equations (1) and (2).  You will get\r\n" );
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document.write( "     3x    = -1;   hence  x = .\r\n" );
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document.write( "Next, from equation (1) express  y = x + m = .\r\n" );
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document.write( "Now, substitute both these expressions  x =   and  y =   into equation (3).  You will get\r\n" );
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document.write( "     +  = 4m + 1.    (4)\r\n" );
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document.write( "You just have one equation for one single unknown m in both sides.   It is easy to solve.\r\n" );
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document.write( "So, multiply equation (4) by 3 (both sides) to run from denominator.  You will get\r\n" );
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document.write( "    -1 + 15m - 5 = 12m + 3\r\n" );
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document.write( "         15m - 6 = 12m + 3\r\n" );
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document.write( "          3m     = 3 + 6 = 9\r\n" );
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document.write( "           m             = 9/3 = 3.\r\n" );
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document.write( "ANSWER.  m = 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Quite simple and reasonably short. Isn't it ?\r
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\n" ); document.write( "\n" ); document.write( "The strategy was to construct equation for single unknown \"m\" and then solve it.\r
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\n" ); document.write( "\n" ); document.write( "Also notice that as soon as you found \"m\", you can find x and y momentarily\r
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document.write( "    x =    (you just know it);   y =  =  = 2  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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\n" ); document.write( "\n" ); document.write( "Ignore the post by @josgarithmetic, since his solution is INCORRECT.\r
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