In parallelogram DEFG, DH = x + 1 HF = 3y GH = 3x - 4, and HE = 5y + 1 Find the values of x and y. The diagram is not drawn to scale.
Since DEFG is a parallelogram, we know that opposite sides are equal in length.
Since DH = HF, we have x + 1 = 3y.
Since GH = HE, we have 3x - 4 = 5y + 1.
We now have the following system of equations:
x + 1 = 3y
3x - 4 = 5y + 1
To solve this system, we can rearrange the first equation to solve for x:
x = 3y - 1
Substituting this value of x into the second equation, we have:
3(3y - 1) - 4 = 5y + 1
Expanding and simplifying, we get:
9y - 3 - 4 = 5y + 1
9y - 7 = 5y + 1
Subtracting 5y from both sides, we get:
4y - 7 = 1
Adding 7 to both sides, we get:
4y = 8
Dividing both sides by 4, we get:
y = 2
Substituting this value of y back into the first equation, we have:
x + 1 = 3(2)
x + 1 = 6
x = 5
Therefore, the values of x and y are x = 5 and y = 2.