http://imageshack.us/a/img600/9208/46482438201155754pm1773.png
If ON = 8x – 8, LM = 7x + 4, NM = x – 5, and OL = 3y – 6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.

Question

http://imageshack.us/a/img600/9208/46482438201155754pm1773.png
If ON = 8x – 8, LM = 7x + 4, NM = x – 5, and OL = 3y – 6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.

hartnn · Answer

hint : opposite sides of parallelogram are equal.

hartnn · Answer

so, ON =LM
can u form an equation ?

zeig_101 · Answer

8x-8=7x+4

hartnn · Answer

thats correct! 
now can u solve that for x ?

zeig_101 · Answer

8x=7x+12
x=12

hartnn · Answer

very good! 
now other pair of opposite side is also equal.
NM =OL
equation ?

anonymous · Answer

Great work zeig_101

zeig_101 · Answer

NM = x – 5, and OL = 3y – 6,
x-5=3y-6
12-5=3y-6
7=3y-6
13=3y

zeig_101 · Answer

y=4.3333333

anonymous · Answer

You are in the right way zeig_101.

hartnn · Answer

yes , you are $\large \checkmark$

zeig_101 · Answer

is that all I need?

hartnn · Answer

yes, you can keep, y= 13/3 or 4.3333 is also ok.

zeig_101 · Answer

so y=4.repeated 3, and x=12?

hartnn · Answer

yes, exactly.