Question

In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Find the values of x and y.

Answer 1

Where did the H come from? Missing info?

Answer 2

its the middle of the parallelogram

Answer 3

First step is always to draw it out. I'll help you here

Answer 4

thats how it look

Answer 5

yea !! yours look better

Answer 6

From the diagram, you can see DH = HF
You can form your first equation here

Answer 7

After that, GH = HE
That would be your second equation

Answer 8

You have two equations and two unknowns. Solve simultaneuosly

Answer 9

so x+3=3y

Answer 10

yes. that is your first equation

Answer 11

whats next

Answer 12

Find your second equation. I told you how already

Answer 13

The main thing here is that H is the midpoint of the diagonals. So, half the diagonals would be equal to each other

Answer 14

H is midpoint of GE. SO GH = HE

Answer 15

i did that already

Answer 16

so, what are your two equations?

Answer 17

x+3=3y and 3x-3=5y+4

Answer 18

yup. Do you know how to solve simultaneous equations? Using substitution or elimination?

Answer 19

alittle

Answer 20

but the y and x together throws me off

Answer 21

K I'll show you step - by -step

Answer 22

ok

Answer 23

x + 3 = 3y --> eqn (1)
3x- 3 = 5y + 4 --> eqn (2)

Answer 24

From (1),
x = 3y - 3 --> (3)

Answer 25

Substitute x = 3y - 3 into equation (2)

3(3y-3) - 3 = 5y + 4

Answer 26

Can you solve for y now?
Then substitute the value of y into equation 1, 2 or 3 and solve for x

Answer 27

would i combine like terms?

Answer 28

3(3y - 3) -3 = 5y + 4
9y - 9 - 3 = 5y + 4
bring y over to one side and the numbers on the other side

Answer 29

i think i messed up