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. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.
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. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.

User Phil Mok
by
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1 Answer

5 votes
In a parallelogram, opposite sides are congruent.

This means that
LM = ON
NM = OL

Using the equations, find x and y:
4x - 6 = 3x + 5
4x = 3x + 11
1x = 11
x = 11

x - 4 = 4y - 3
x - 1 = 4y
-1 = 3y
-1/3 = y

The values are:
x = 11
y = -1/3
User Jordanthompson
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User Naxchange
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Naxchange asked Jun 13, 2024
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