20 points if o n = 8 x − 8 , l m = 7 x + 4 , n m = x − 5 , and o l = 3 y − 6 , find the values of x and y for which lmno must be a parallelogram.

To find x:

ON is parallel to LM

8x - 8 = 7x + 4

-7x        -7x

1x - 8 = 4

     +8   +8

1x = 12

---    ---

1        1

x = 12

8(12) - 8 = 7(12) + 4

96 - 8 = 84 + 4

88 = 88

To find y:

NM is parallel to OL

x - 5 = 3y - 6

12 - 5 = 3y - 6

7 = 3y - 6

+6      +6

13 = 3y

---    ---

3      3

13/3 = y

Check:

12 - 5 = 3(13/3) - 6

7 = 13 - 6

7 = 7

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