if ON = 7x-6, LM = 6x+9, NM = x+8, and OL=3y-5, find the values of x and y for which LMNO must be a parallelogram.

The value of x is 3 and the value for y is 16/3

Step-by-step explanation:

First, to find the value of x, we can set LM equal to ON. This is because they are opposite sides of a parallelogram, which means they must be the same length.

LM = ON

6x + 9 = 7x + 6

Now we can solve for x.

6x + 9 = 7x + 6

9 = x + 6

3 = x

Now that we have a value for x, we can find the value of y. For the same reason as stated above, OL and NM must be equal.

OL = MN

3y - 5 = x + 8

Now since we know that x = 3, we can substitute in and solve for y.

3y - 5 = x + 8

3y - 5 = 3 + 8

3y - 5 = 11

3y = 16

y = 16/3