Question

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

DH = HF

Answer 2

and

GH = HE

Answer 3

Look at the diagonals Part

http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/index.php#diagonalParallelogram

Answer 4

So set up those two equations

Answer 5

DH = HF

x + 1 = 3y

and ...

Answer 6

Here's a marked up diagram of this problem. It may help.

Answer 7

Hello directrix!

Answer 8

X+1 = 3Y
3X-4 =5Y +1

Answer 9

yeah, can you solve those for x and y?

Answer 10

Doing a little rearranging...

X - 3Y = -1
3X - 5Y = 5

Answer 11

Multiply the first equation by (-3)......

-3X + 9Y = 3
3X - 5Y = 5

Answer 12

Add them together now....

0X + 4Y = 8

Answer 13

0x?

Answer 14

so you get..

4Y = 8, or Y = 2

Answer 15

yeah when you add the two equations together, you get -3x + 3x = 0x

Answer 16

yes

Answer 17

wouldint just be X

Answer 18

What do you mean?

Answer 19

oh! i get it

Answer 20

The reason we multiplied the first equation through by (-3) was that so when you add them, the X term cancels out , so you can solve for Y

Answer 21

ahh, cool

Answer 22

So now that you figured out one of the variables Y, you can use Y=2 in either of the two equations to get your X value

Answer 23

Equation 1

X - 3Y = -1 Y=2

X - 3(2) = -1

X - 6 = -1

X = -1 + 6

X=5

Answer 24

You understand everything?

Answer 25

yea

Answer 26

1) THe diagonals of a parallelogram are bisected
2) Solving a system of equations with 2 variables

Answer 27

awesome

Answer 28

?