﻿ Intersection of two lines

The intersection of two lines is the unique point (x,y) that the two lines meet.  In order to find this point (x.y) we use simultaneous equations or do it graphically.

L: 2x - y = 0 and K: x + 2y= 5.  Find the coordinates of the point of intersection?

 Solving it graphically, You can draw both lines.  In order to draw a line you must plug in values for each coordinate. X+2y=5 Put 0 in for X  to give 0+2y=5 =>  y=2.5   First Pt is (0, 2.5) Put 0 in for Y to give  X+0=5 => X=5   Second Pt is (5,0) 2X-Y=0 Put 0 in for X to give 0-y=0 => y=0     First Pt (0,0) Put 2 in for Y to give 2x-2=0 => x=1    Second Pt (1,2)

Draw both lines and the point of intersection can be seen to be (1,2)

Algebraic Solution

 There are two unknowns so we must get rid of one.  Lets get the LCM of x or y whatever is the easiest.  In this case  it is 2 with both of them. 2x - 1y = 0  1x + 2y = 5 To get rid of the X.  We must multiply the bottom equation by 2 2x - y = 0  2x+4y=10 In order to get rid of x now we must subtract the equations.  To subtract we just change the sign of all the items on the lower line and add. 2x - y =     0 -2x - 4y  = -10                                         -5y = -10                ==> y=2 Now we must plug y into one of the equations to find x 2x - y = 0    2x - 2 = 0                                       2x=2                 ==> x=1 Therefore the point of intersection is (1,2)