if ON=7x-5, LM= 6x+3, NM =x-4, and OL =2y+5, find the value of x and y given that LMNO is a parallelogram
if ON=7x-5, LM= 6x+3, NM =x-4, and OL =2y+5, find the value of x and y given that LMNO is a parallelogram
4x
To find the values of x and y in the parallelogram LMNO, we can use the properties of parallelograms.
A key property of a parallelogram is that opposite sides are equal in length. In this case, we have ON = LM and NM = OL.
Given that ON = 7x - 5 and LM = 6x + 3, we can set up the equation:
7x - 5 = 6x + 3
To solve for x, we can first subtract 6x from both sides:
7x - 6x - 5 = 3
This simplifies to:
x - 5 = 3
Then, add 5 to both sides:
x - 5 + 5 = 3 + 5
This simplifies to:
x = 8
So, the value of x is 8.
Now let's calculate the value of y using the fact that NM = OL.
Given that NM = x - 4 and OL = 2y + 5, we can set up the equation:
x - 4 = 2y + 5
To solve for y, we can first subtract 5 from both sides:
x - 4 - 5 = 2y
This simplifies to:
x - 9 = 2y
Then, divide both sides by 2:
(x - 9) / 2 = y
So, the value of y is (x - 9) / 2. Substituting the value of x we found earlier, y = (8 - 9) / 2.
Simplifying further:
y = -1 / 2
Therefore, the value of x is 8 and the value of y is -1/2 in the parallelogram LMNO.
Look how very similar your question is to Lisa's
http://www.jiskha.com/display.cgi?id=1333684299
Follow the solution I gave her.