#### lost and found

##### New member
The problem ask "to find the values of x and y that ensure quadriliteral is parallelogram.
First one looks like this:
Code:
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/     /
/     /
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In a bigger version. The left parallel side is said to have a value of 4. The site oposite to that one is 4x-y. The top side is 3x+17 and the bottom one is 2y. I don't understand how to create an eduation and solve it. I knowt the sides are parallel and they are suppose to be equal but I can't create an equation. How am I suppose to solve this?

#### Gene

##### Senior Member
It's a strange way of presenting it but I think they want you to solve
4x-y=4 and
2y=3x+17
to find an x and y that makes them true.

#### lost and found

##### New member
yes i just don't really know how to solve thoese equations... i mean there are two varuables...

#### Denis

##### Senior Member
lost and found said:
yes i just don't really know how to solve thoese equations... i mean there are two varuables...
4x-y=4 and
2y=3x+17

4x - y = 4 [1]
3x -2y= -17 [2] : follow that?

***Multiply [1] by -2:
-8x + 2y = -8 [1]
3x - 2y = -17 [2]

-5x = -25

Can you finish it?

***we could multiply by 2, then subtract the 2 equations: same result.
The intent is to rearrange so we can eliminate one variable.

Here's an example:
3x + 2y = 16 [1]
5x - 3y = -5 [2]

Multiply [1] by 3 and [2] by 2:
9x + 6y = 48 [1]
10x - 6y = -10 [2]

See what happens to the y terms?
19x = 38
x = 2

Now substitute x = 2 in [1]
3(2) + 2y = 16
6 + 2y = 16
2y = 16 - 6
2y = 10
y = 5