Question

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.

Answer 1

x=12 and y=13/3

Explanation:

!!This is the right answer, other one the math is wrong!!

For a parallelogram, opposite sides must be equal.

ON = LM

8x-8 = 7x+4

x = 12

OL = NM

3y-6 = x-5

3y-6 = 12-5

3y = 13

y = 13/3

Answer 2

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,

`8x * 8 = 7x + 4`
Simplify

`64x = 7x + 4`
subtract 7x from both sides

`57x = 4`
divide 57 from both sides

`x = (4)/(57)`
Substitute x into equations

`8x * 8 = 7x + 4 = 4 (28)/(57)`


`3y - 6 = x - 5`

`3y - 6 = 4 (28)/(57) - 5`

`3y - 6 = - (28)/(57)`
NM & OL = -28/57
ON & LM = 4 + (28/57)