# The Straight Line

• Aug 31st 2008, 08:10 AM
mattymaths
The Straight Line
Three lines have the equations 2x+3y-4=0
3x-y-17=0
x-3y-10=0

Show wether these lines are cocurrent or not.

Anyone know how to do this, darn im rubbish at maths (Wait)
• Aug 31st 2008, 08:29 AM
Soroban
Hello, mattymaths!

Quote:

Given three lines: . $\begin{array}{cccc}2x+3y-4&=&0 &{\color{blue}[1]}\\ 3x-y-17&=&0 & {\color{blue}[2]}\\ x-3y-10&=&0 &{\color{blue}[3]}\end{array}$

Show whether these lines are concurrent or not.

"Concurrent" means they intersect at one point.

Find the intersection of [1] and [3].
Find the intersection of [2] and [3].

Are they the same point?

• Aug 31st 2008, 09:54 AM
mattymaths

Would i be right then rearranging the equations [1] and [2] so they look like
2x+3y=4
3x-y=17

and then solving simultaneously?
Then doing the same for [2] and [3]?
• Aug 31st 2008, 10:03 AM
Soroban

Yes . . . absolutely right!

• Aug 31st 2008, 10:19 AM
mattymaths
I thought that, but i just cant seem to get it right, can you see where im going wrong?

[1] 2x + 3y = 4
[2] 3x -y = 17 X3

[1] 2x + 3y=4
[2] 9x - 3y=51

11x=55?

doesnt seem to work out right, i'm not too sure what ive done wrong (Worried)

SORRY I'VE NOTICED MY INCREDIBLY SILLY MISTAKE!

Anyway i done 2(5)+3y=4
so 10+3y=4
3y=4-10
3y=-6
y=-2

so (5,-2) is this right? i hope so ha!

Thank you very much for the replies btw