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.

Answer 1

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.