**Mathematics Problem: Parallelogram Properties**Given the equations:\[ ON = 7x - 5 \]\[ LM = 6x + 3 \]\[ NM = x - 4 \]\[ OL = 2y + 5 \]**Problem:**Find the values of $ x $ and $ y $ given that LMNO is a parallelogram.**Solution:**To find the values of $ x $ and $ y $, we use the property that in a parallelogram, opposite sides are equal in length.Therefore, we have:1. $ ON = LM $2. $ NM = OL $From the first pair of equations:\[ 7x - 5 = 6x + 3 \]Solving for $ x $:\[ 7x - 6x = 3 + 5 \]\[ x = 8 \]From the second pair of equations:\[ x - 4 = 2y + 5 \]Substitute $ x = 8 $:\[ 8 - 4 = 2y + 5 \]\[ 4 = 2y + 5 \]Solving for $ y $:\[ 4 - 5 = 2y \]\[ -1 = 2y \]\[ y = -\frac{1}{2} \] Thus, the values are $ x = 8 $ and $ y = -\frac{1}{2} $.

Name: **Mathematics Problem: Parallelogram Properties**Given the equations:
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Description: **Mathematics Problem: Parallelogram Properties**Given the equations:\[ ON = 7x - 5 \]\[ LM = 6x + 3 \]\[ NM = x - 4 \]\[ OL = 2y + 5 \]**Problem:**Find the values of $ x $ and $ y $ given that LMNO is a parallelogram.**Solution:**To find the va

Here given as LMNO is a parallelogram And ON=7x-5, LM=6x+3, NM=x-4, OL=2y+5

Answered: If ON = 7x- 5, LM = 6x + 3, NM =x- 4,…

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If ON = 7x- 5, LM = 6x + 3, NM =x- 4, and OL = 2y + 5, find the values of x and y given that LMNOIS a parallelogram.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

**Mathematics Problem: Parallelogram Properties**

Given the equations:
\[ ON = 7x - 5 \]
\[ LM = 6x + 3 \]
\[ NM = x - 4 \]
\[ OL = 2y + 5 \]

**Problem:**
Find the values of $ x $ and $ y $ given that LMNO is a parallelogram.

**Solution:**
To find the values of $ x $ and $ y $, we use the property that in a parallelogram, opposite sides are equal in length.

Therefore, we have:
1. $ ON = LM $
2. $ NM = OL $

From the first pair of equations:
\[ 7x - 5 = 6x + 3 \]
Solving for $ x $:
\[ 7x - 6x = 3 + 5 \]
\[ x = 8 \]

From the second pair of equations:
\[ x - 4 = 2y + 5 \]
Substitute $ x = 8 $:
\[ 8 - 4 = 2y + 5 \]
\[ 4 = 2y + 5 \]
Solving for $ y $:
\[ 4 - 5 = 2y \]
\[ -1 = 2y \]
\[ y = -\frac{1}{2} \]

Thus, the values are $ x = 8 $ and $ y = -\frac{1}{2} $.

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