The values of the variable are 3 and 6.
Explanation:
In parallelogram RECT is a rectangle,
EC = x + y , RT = 2x - y, RE = 2x + y and TC = 3x - 3
To find, the values of the variable = ?
∵ The opposite sides are equal.
∴ RE = TC and RT = EC
2x + y = 3x - 3
⇒ x - y = 3 .......... (1)
Also,
2x - y = x + y
⇒ x - 2y = 0 .......... (2)
Subtracting (1) from (2), we get
∴ x - y - (x - 2y ) = 3 - 0
⇒ x - y - x + 2y = 3
⇒ y = 3
Put y = 3 in equation (1), we get
x - 3 = 3
⇒ x = 3 + 3 = 6
∴ x = 6 and y = 3
Thus, the values of the variable are 3 and 6.