Question

I am getting the wrong answers and I don't know where I am going wrong! Please help!
4. The line with the equation 5x+y=20 meets the x axis at A and the line with the equation x+2y=22 meets the y axis at B. The two lines intersect at point C.
(iv) Find the co-ordinates of the point E such that ABEC is a parallelogram.
This is what I have done (I don't know if this is right or not):
I have found the gradient of BA ( -11/4) which I know will be parallel to EC. I then use the point (0,11) to find the equation of the line BA. I get 4y+11x=44 from this.
I do the same for CA (parallel to EB) .

Answer 1

It wouldnt let me type any more so heres the rest

Answer 2

I get -5 for the gradient and use point C (2,10) to get the equation of the line 5x+y=20

Answer 3

I solve the two equations simultaneously to find where they intersect and only get through the first part till I get -9x=56 which I already know is wrong since x has to equal -2

Answer 4

I can post a picture of everything too

Answer 5

The first line: 5x +y =20 (1), A on this line and A (4,0)
The second line : x+2y = 22 (2) , B on this line and B (0,11)
Ok??

Answer 6

Yes

Answer 7

C (2,10) ok?

Answer 8

Ok.

Answer 9

now, if it forms a parallelogram, then the left side is

Answer 10

Oh wait i think you have A and B wrong.

Answer 11

Show me my mistake, please.

Answer 12

This is the answer for the first question it asked saying what the graph looks like

Answer 13

So B is on the line on the bottom and is is on the line to the left

Answer 14

yes, just estimate. As long as my logic is Ok, I am ok.

Answer 15

Ok :)

Answer 16

agree with me for this?

Answer 17

Yes, I think so

Answer 18

That is I need a line parallel to 5x+y =20 and passes through B, right?

Answer 19

Now, calculate that line by plugging B coordinate in the equation, I get
\(5\color{red}{x}+\color{blue}{y}=20\\5\color{red}{0}+\color{blue}{11}=11\), Hence my new line has the equation 5x +y =11