document.write( "Question 1065633: What is the x-coordinate of the point where the lines x=4y-8 and 12x+y=11 intersect? \n" ); document.write( "

Algebra.Com's Answer #680802 by math_helper(2461) $\"\"$ $\"About$

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I like to work with the slope-intercept form of the line:\r
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document.write( "   x=4y-8  —>    y = (1/4)x + 2       (1)\r\n" );
document.write( "   12x+y=11  —>   y = -12x + 11       (2)\r\n" );
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document.write( "At the point where they intersect the two y values must be equal, so set eq(1) = eq(2):\r\n" );
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document.write( "        (1/4)x + 2 = -12x + 11\r\n" );
document.write( "        ( (1/4) + (48/4))x = 9\r\n" );
document.write( "               (49/4)x = 9\r\n" );
document.write( "                         x  = 36/49\r\n" );
document.write( "—\r\n" );
document.write( " Ans:  \r\n" );
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document.write( "Check:   Plug in x=36/49 to eq(1) and eq(2) to make sure they produce identical y values:\r\n" );
document.write( "(1)   y = (1/4)(36/49) + 2 = (9/49) + (98/49) = 107/49\r\n" );
document.write( "(2)   y  = -12(36/49) + 11 = (-432/49) + (539/49) = 107/49  (they match)\r\n" );
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