Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are :

Solution:

(i) The given equations are 

$y=x$....(i)

$y=2 x$...(ii)

$y+x=6$...(iii)

It is seen that the coordinates of the vertices of the obtained triangle are $A(0,0), \mathrm{B}(2,4), \mathrm{C}(3,3)$

(ii) The given equations are 

$y=x$....(1)

$3 y=x$...(11)

$x+y=8$....(111)

The two points satisfying (i) can be listed in a table as,

It is seen that the coordinates of the obtained triangle are $A(0,0), B(4,4), C(6,2)$