Question

Show graphically that each one of the following systems of equations has infinitely many solutions:

3x + y = 8

6x + 2y = 16

Answer 1

The given equations are

3x + y = 8  ....(i)

6x + 2y = 16 .....(ii)

Putting x = 0 in equation  (i) we get

`=> 3 xx 0 + y = 8`

`=> y = 8`

x = 0, y = 8

Putting y = 0 in equations (i) we get

`=> 3x + 0 = 8`

=> x = 8/3

x = 8/3, y = 0

Use the following table to draw the graph.

x	0	8/3
y	8	0

Draw the graph by plotting the two points A(0, 8) and B(8/3, 0) from table

Graph of the equation...(ii)

6x + 2y = 16 ....(ii)

Putting x = 0 in equation (ii) we get

`=> 6 xx 0 + 2y = 16`

`=> y = 8`

x= 0, y = 8

Putting y = 0 in equation (ii) we get

`=> 6x + 2 xx 0 = 16`

`=> x = 8/3`

x = 8/3, y = 0

x	0	8/3
y	8	0

Draw the graph by plotting the two points C(0,8), D(8/3, 0) from table.

Thus the graph of the two equations coincide

Consequently, every solution of one equation is a solution of the other.

Hence the equations have infinitely many solutions.