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. The drawing is not to scale.
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Y=
To determine the values of x and y for which ABCD must be a parallelogram, we need to find a relationship between the opposite sides of the quadrilateral.
First, we can see that AE = DC and DE = AB, so we need to set these expressions equal to each other.
AE = DC
3x - 6 = 6y - 12
Next, we can set up an equation using the opposite sides DE and BC.
DE = BC
6y - 12 = 2y + 24
Now we have a system of equations:
3x - 6 = 6y - 12
6y - 12 = 2y + 24
Let's solve this system of equations:
From the first equation, we can simplify:
3x = 6y - 6
x = 2y - 2
We substitute this expression for x into the second equation:
6y - 12 = 2y + 24
Combine like terms:
4y = 36
y = 9
Now we can substitute this value for y into the expression for x:
x = 2(9) - 2
x = 18 - 2
x = 16
So, the values of x and y for which ABCD must be a parallelogram are:
X = 16
Y = 9