In the given parallelogram
From the property of diagonals of Parallelogram
The diagonals are bisect each other into equal parts
So, according to the figure
length 2x= length of y
2x=y
Similarly for the second diagonal,
length y+4=length3x
y+4=3x
Simplify the both equation by substitution method,
In substitution method, substitute the value of any one varibale and put into the another equation and simplify
[tex]\begin{gathered} 2x=y \\ y=2x \\ \text{Substitute the value of y into the other equation} \\ y+4=3x \\ 2x+4=3x \\ 3x-2x=4 \\ x=4 \end{gathered}[/tex]
Now substitute the value of x=4 into the first equation and simplify for y
[tex]\begin{gathered} x=4 \\ 2x=y \\ 2(4)=y \\ y=8 \end{gathered}[/tex]
So the value of varriables x = 4 and y=8
Answer : A) x=4, y=8
