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.

ON = 8x • 8
LM = 7x + 4
NM = x - 5
OL = 3y - 6

OL is congruent & parallel to NM
LM is congruent & parallel to ON

So,
[tex]8x \times 8 = 7x + 4[/tex]
Simplify
[tex]64x = 7x + 4[/tex]
subtract 7x from both sides
[tex]57x = 4[/tex]
divide 57 from both sides
[tex]x = \frac{4}{57} [/tex]
Substitute x into equations
[tex]8x \times 8 = 7x + 4 = 4 \frac{28}{57} [/tex]

[tex]3y - 6 = x - 5[/tex]
[tex]3y - 6 = 4 \frac{28}{57} - 5[/tex]
[tex]3y - 6 = - \frac{28}{57} [/tex]
NM & OL = -28/57
ON & LM = 4 + (28/57)