Question 306433
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How do you find the values of x and y that ensure {{{highlight(cross(eace))}}} <U>that</U> 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.
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Regarding this problem, tutor @Theo expresses perplexity.
Meanwhile, its meaning is clear and the solution is simple.


<pre>
The necessary and sufficient condition for a quadrilateral to be a parallelogram is that
the opposite sides are congruent, i.e. have equal length.


It gives us two equations

    2x-4 = 10      for the top and the bottom sides,

    -3y = 12 - y   or the left and right sides.


From the first equation 

    2x = 10 + 4 = 14  --->  x = 14/2 = 7.


From the second equation

    -3y + y = 12  --->  -2y = 12  --->  y = 12/(-2) = -6.


<U>ANSWER</U>.  x = 7, y = -6.
</pre>

Solved.