Answer: The value of x and y is 5 and 2 respectively.
Step-by-step explanation:
Since we know that "Diagonals of parallelogram bisects each other":
So, we have given that
in parallelogram DEFG,
DH = x + 1, HF = 3y, G H = 3 x − 4 , and HE = 5y + 1.
so, According to question, as shown in the figure below:
[tex]DH=HF\\\\x+1=3y\\\\x-3y=-1-----------(1)[/tex]
Similarly,
[tex]GH=HE\\\\3x-4=5y+1\\\\3x-5y=1+4\\\\3x-5y=5----------------(2)[/tex]
Using Substitution Method to solve system of equation:
From eq(1), we get
[tex]x=-1+3y[/tex]
Putting the value of x in eq (2), we get
[tex]3x-5y=5\\\\3(-1+3y)-5y=5\\\\-3+9y-5y=5\\\\4y=5+3\\\\4y=8\\\\y=\frac{8}{4}\\\\y=2[/tex]
Now,, put the value of y to get the value of x:
[tex]x=-1+3y\\\\x=-1+3(2)\\\\x=-1+6\\\\x=5[/tex]
Hence, the value of x and y is 5 and 2 respectively.
