Intersection of lines

To find the point of intersection of two lines (i.e. the place where they cross each other) we use simultaneous equations.

 

Example:

Find the point of intersection of A:2x+3y=-11 & B:4x-y=-1   

A:   2x + 3y =-11 » write down both lines

B:   4x  -   y = -1

    under each other     
A:   2x + 3y =-11    » eliminate y by multiplying 
B: 12x  - 3y = -3      line B by 3

       14x =-14     

 » add like values together
           x = -1     » divide by 14 to find x value 

Sub the x-value (x=-1) back into the original equation to find the y-value.

A:    2(-1) + 3y = -11 
            -2 + 3y = -11

                   3y = 11 + 2

                   3y = 9
                    y = 3

The point of intersection of these two lines is (-1,3)

 

 

IMPORTANT

If the line intersects the x-axis then y=0

If the line intersects the y-axis then x=0

 

Example:

Find the point of intersection of L:2x+6y=12 at x and y axes

1.  If L intersects the x-axis then y=o
        2x + 6y = 12
        2x + 6(0) = 12
        2x = 12

          x = 6              Point of intersection: (6,0)

 

2.   If L intersects the y-axis then x=o

        2x   + 6y = 12

        2(0)+ 6y = 12
            0 + 6y = 12
                   y = 2     Point of intersection: (0,2)

 

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