Point of Intersection Question6

In this page Point of Intersection Question6 we are going to see solution of second question in the worksheet point of intersection.

What does mean by point of intersection:

If two straight lines are not parallel then they will meet at a point.This common point for both straight lines is called the point of intersection.If the equations of two intersecting straight lines are given,then their intersecting point is obtained by solving equations simultaneously. Find the intersection point of the straight lines 5 x + 6 y = 25  and

3 x - 4 y = 10

Solution:

5 x + 6 y = 25 ----- (1)

3 x - 4 y = 10  ------(2)

In the first equation coefficient of x is 5,in the second equation the coefficient of x is 3 and we have same signs for both equations. But the coefficient of y in the first equation is 6 and coefficient of y in the second equation is -4 and we have same signs.

To make the coefficient of y of the first equation as 12 we need to multiply the the whole equation by 2.To make the coefficient of y of the second equation as 12 we need to multiply the the whole equation by 3.

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

(1) x 2 = >            10 x + 12 y = 50

(2) x 3 = >             9 x - 12 y = 30

10 x + 12 y = 50

9 x - 12 y = 30

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

19 x   = 80

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

x = 80/19

Substituting x = 80/19 in the first equation

5 (80/19) + 6 y = 25

400/19 + 6 y = 25

(400+114y)/19 = 25

400 + 114 y = 25 x 19

400 + 114 y = 475

114 y = 475 - 400

114 y = 75

y = 75/114

y = 25/38

So the intersection point of the straight lines is (80/19,25/38) .Point of Intersection Question6  Point of Intersection Question6

 Questions Solution (1) Find the intersection point of the straight lines   x - 5y + 17 =0  and 2x + y + 1 = 0 Solution (2) Find the intersection point of the straight lines   5 x - 3 y - 8 = 0  and 2x - 3 y - 5  = 0 (3) Find the intersection point of the straight lines   4 x - 7 y =0  and 8 x - y - 26 = 0 Solution (4) Find the intersection point of the straight lines   3 x + 5 y - 6 =0  and 5 x - y - 10 = 0 Solution (5) Find the intersection point of the straight lines 2 x + 3 y =5  and 3 x + 4 y = 7 Solution (7) Find the intersection point of the straight lines   4 x - 3 y = 3  and 3 x + 2 y = 15 Solution (8) Find the intersection point of the straight lines   3 x + 2 y = 11 and 7 x - 3 y = 41 Solution (9) Find the intersection point of the straight lines   5 x + 3 y = 11  and 3 x + 5 y = -3 Solution (10) Find the intersection point of the straight lines   2 x - y = 15  and 5 x + 3 y = 21 Solution

Point of Intersection Question6 to Analytical Geometry 