If ON = 9x - 8, LM = 8x + 4, NM = x - 8, and OL = 3y - 5, find the values of x and y for which LMNO must be a parallelogram.

x is 12 and y is 3

Step-by-step explanation:

Given a parallelogram LMNO,

LM = ON and OL = NM

Given;

ON = 9x - 8

LM = 8x + 4

NM = x - 8, and

OL = 3y - 5

Substitute into the expression

LM = ON

8x + 4 = 9x - 8

8x - 9x  = -8 - 4

-x  = -12

x = 12

Also OL = NM

3y - 5 = x - 8

3y - 5 = 12-8

3y - 5 = 4

3y = 4+5

3y = 9

y = 9/3

y = 3

Hence the value of x is 12 and y is 3