4. deck is a parallelogram. find the values of x and y.
kt = 2x + y
dt = x + 2y
te = 12
tc = 9

The value of  x  = 5 and y = 2.

Step-by-step explanation:

Here, given DECK is a parallelogram.

Also, KT = 2x + y  , DT = x + 2y  , TE = 12   and TC = 9

Now, in parallelogram:

DIAGONALS IN A PARALLELOGRAM BISECT EACH OTHER

Also, in the parallelogram DECK,

Sides DC and KE are two diagonals.

⇒ T is the mid point of AC and KE.

⇒ KT = TE and DT = TC ( as diagonals are bisected)

⇒  2 x +   y =  12 and x  +  2y = 9

So here, the set of two equations are:

2 x +   y = 12   (1)

x  +  2 y = 9   (2)

Multiply (2) with -2 and add with (1), we get:

2 x +  y  - 2 x - 4 y = 12  - 18

or, - 3 y = - 6

or, y = 2

If y = 2, then x  +  2 (2) = 9 or, x  = 5

Hence the values of  x  = 5, y = 2

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step-by-step explanation: vsfdvsfvd