Question

Show graphically that the following system of equations has infinitely many solutions:

x – 2y + 11 = 0

3x – 6y + 33 = 0

Answer 1

The given equations are

x − 2y + 11 = 0   ...........(i)

3x − 6y + 33 = 0  .......(ii)

Putting x = 0 in equation (i) we get

`=> 0 - 2y = -11`

`=> y = 11/2`

`x =  0, y = 11/2`

Putting y = 0 in equation (i) we get

`=> x - 2x = -11`

`=> x = -11`

x = –11, y = 0

Use the following table to draw the graph.

x	0	–11
y	`11/2`	0

Draw the graph by plotting the two points A`(0, 11/2)`, B(–11, 0) from table.

Graph of the equation .....(ii)

3x – 6y = –33   ....(ii)

Putting x = 0 in equation (ii) we get

`=> 3 xx 0 - 6y = -33`

`=> y = 11/2`

`x = 0, y = 11/2`

Putting y = 0 in equation (ii) we get

`=> 3x - 6 xx 0 = -33`

`=> x = -11`

x = –11, y = 0

Use the following table to draw the graph.

x	0	–11
y	`11/2`	0

Draw the graph by plotting the two points C`(0, 11/2)`, D(–11, 0) from table.

Thus the graph of the two equations are coincide

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

Hence the equations have infinitely many solutions.