Here,

Let's take the equation :

y = -13x -7 as Line 1

y= -x + 5 as Line 2

y = x - 7 as Line 3

We need to find out the point of intersection of these 3 lines

Line 1 and Line 2 meets when x = -1 and y = 6

Line 2 and Line 3 meets when x = 6 and y = -1

Line 1 and Line 3 meets when x = 0 and y =-7

(I have not shown the calculation)

The fig shown below.

Now to find out the area from the 3 lines combined, lets make it a rectangle with co-ordinates (-1,6), (-1,-7) , (6, -7) and (6,6)

Now we need to find out the area of the three right angled triangles formed , they are yellow \(\triangle\) , green \(\triangle\) and purple \(\triangle\)

For green \(\triangle\),

Base = 1 , height = 13

Area = \(\frac{1}{2} *1 * 13 = \frac{13}{2}\)

For purple \(\triangle\)

Area = \(\frac{1}{2} *6 * 6 = 18\)

For Yellow \(\triangle\)

Area = \(\frac{1}{2}*7 * 7 = \frac{49}{2}\)

Now the area of the rectangle = \(13 * 7 = 91\)

Hence the Area formed by 3 lines =\(91 - (\frac{13}{2} + 18 + \frac{49}{2}) = 42\)

_________________

Great explanation, Sir
_________________

Can you plz share the Source

Thank you
_________________

Source is the Green GRE-1 book from Jamboree.

Thank you for such a great explanation sir.

thanks for the answer

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.