document.write( "Question 306433: How do you find the values of x and y that ensure eace quadrilateral is a parallelogram? The top is 2x-4, the bottom is 10, the left side is -3y and the right side is 12-y. \n" ); document.write( "

Algebra.Com's Answer #852417 by ikleyn(53017) $\"\"$ $\"About$

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\n" ); document.write( "How do you find the values of x and y that ensure $\"highlight%28cross%28eace%29%29\"$ that quadrilateral is a parallelogram? \r
\n" ); document.write( "\n" ); document.write( "The top is 2x-4, the bottom is 10, the left side is -3y and the right side is 12-y.
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\n" ); document.write( "\n" ); document.write( "Regarding this problem, tutor @Theo expresses perplexity.
\n" ); document.write( "Meanwhile, its meaning is clear and the solution is simple.\r
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document.write( "The necessary and sufficient condition for a quadrilateral to be a parallelogram is that\r\n" );
document.write( "the opposite sides are congruent, i.e. have equal length.\r\n" );
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document.write( "It gives us two equations\r\n" );
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document.write( "    2x-4 = 10      for the top and the bottom sides,\r\n" );
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document.write( "    -3y = 12 - y   or the left and right sides.\r\n" );
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document.write( "From the first equation \r\n" );
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document.write( "    2x = 10 + 4 = 14  --->  x = 14/2 = 7.\r\n" );
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document.write( "From the second equation\r\n" );
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document.write( "    -3y + y = 12  --->  -2y = 12  --->  y = 12/(-2) = -6.\r\n" );
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document.write( "ANSWER.  x = 7, y = -6.\r\n" );
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