If AE=3x-6, DE = 6y-12, EC = 2x+2 and EB = 2y+24, find the values of x and y for which ABCD must be a parallelogram. (4 points) x = y =

Answer 1

In order for ABCD to be a parallelogram, opposite sides must be equal.

We have:

AE = 3x - 6
DE = 6y - 12
EC = 2x + 2
EB = 2y + 24

In a parallelogram, AE = DC and DE = AB.
So, we can set up the following equations:

AE = DC ---> 3x - 6 = 6y - 12
DE = AB ---> 6y - 12 = 2y + 24

Simplifying these equations:

3x - 6 = 6y - 12
6y - 12 = 2y + 24

Subtracting 3x from both sides of the first equation and adding 2y to both sides of the second equation:

-3x + 6 = 6y - 6
2y - 2 = 2y + 24

Simplifying further:

-3x = 6y - 12
2y = 2y + 26

Subtracting 2y from both sides of the second equation:

-3x = 6

Now, we can solve for x:

x = -6 / -3
x = 2

Substituting the value of x into the first equation:

3x - 6 = 6y - 12
3(2) - 6 = 6y - 12
6 - 6 = 6y - 12
0 = 6y - 12

Adding 12 to both sides:

12 = 6y

Dividing both sides by 6:

2 = y

Therefore, x = 2 and y = 2 for ABCD to be a parallelogram.