Concurrency of StraightLines Question10

In this page concurrency of straightlines question10 we are going to see solution of first question on the quiz concurrency of straight lines.

Definition:

If three or more straight lines passing through the same point then that common point is called the point of concurrency

Steps to find whether the three given lines are concurrent:

(i) Solve any two equations of the straight lines and obtain their point of intersection.

(ii) Substitute the co-ordinates of the point of intersection in the third equation.

(iii) Check whether the third equation is satisfied

(iv) If it is satisfied,the point lies on the third line and so the three straight lines are concurrent.           concurrency of straightlines question10  concurrency of straightlines question10

Question 10

Show that the straight lines y - x - 1 = 0,2 x + y + 2 = 0 and

5 x + 3 y + 5 = 0 are concurrent.Find the point of concurrency.

Solution:

The given equations are

-x + y - 1 = 0  ----------(1)

2x + y + 2 = 0  ----------(2)

5 x + 3 y + 5 = 0 ----------(3)

First we need to solve any two equations then we have to plug the point into the remaining equation

In the first equation coefficient of x is -1,in the second equation the coefficient of x is 2 and we have different signs for both equations.But the coefficient of y in the first equation is 1 and coefficient of y in the second equation is 1 and we have different signs.

Then we are going to subtract the first equation from second equation since we have different signs.

-x + y - 1 = 0    ----------(1)

2 x + y + 2 = 0  ----------(2)

(-)   (-)  (-)

----------------

- 3 x - 3 = 0

- 3 x = 3

x = 3/(-3)

x = -1

Substitute x = -1 in the first equation

-x + y - 1 = 0

-(-1) + y - 1 = 0

1 - 1 + y = 0

y = 0

So the point of intersection of the first and second line is (-1,0)

Now we have to apply the point (-1,0) in the third equation 5 x + 3 y + 5 = 0

5 (-1) + 3 (0) + 5 = 0

-5 + 0 + 5 = 0

0 = 0

The third equation is satisfied.So the point (-1,0) lies on the lies on the third line.So the straight lines are concurrent. concurrency of straightlines question10 Questions Solution (1) Show that the straight lines 2 x + y - 1 = 0,2 x + 3 y - 3 = 0 and 3 x + 2 y - 2 = 0 are concurrent.Find the point of concurrency. (2) Show that the straight lines x + y - 5 = 0,3 x - y + 1 = 0 and 5 x - y - 1 = 0 are concurrent.Find the point of concurrency. (3) Show that the straight lines x - y - 2 = 0,3 x + 4 y + 15 = 0 and 5 x - 4 y - 7 = 0 are concurrent.Find the point of concurrency. (4) Show that the straight lines x - 3 y + 3 = 0,2 x + y - 8 = 0 and 5 x - 4 y - 7 = 0 are concurrent.Find the point of concurrency. (5) Show that the straight lines x + y - 7 = 0,2 x + y - 16 = 0 and 3 x + 8 y - 11 = 0 are concurrent.Find the point of concurrency. (6) Show that the straight lines x + y - 3 = 0, x + 2 y - 5 = 0 and x + 3 y - 7 = 0 are concurrent.Find the point of concurrency. (7) Show that the straight lines 3 x + y + 2 = 0,2 x - y + 3 = 0 and x + 4 y - 3 = 0 are concurrent.Find the point of concurrency. (8) Show that the straight lines 3 x - 4 y + 5=0,7 x - 8 y + 5 = 0 and 4 x + 5 y - 45 = 0 are concurrent.Find the point of concurrency. (9) Show that the straight lines x + y - 3 = 0,3 x + 2 y + 1 = 0 and 5 x + 3 y + 5 = 0 are concurrent.Find the point of concurrency. 