Question

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

2x + 3y = 6

4x + 6y = 12

Answer 1

The given equations are

2x + 3y = 6 .....(i)

4x + 6y = 12 ....(ii)

Puting x = 0 in equation (i) we get

`=> 2 xx 0 + 3y = 6`

`=> y = 2`

x = 0, y = 2

Putting y = 0 in equation (i) we get

`=> 2x + 3x = 6`

`=> x = 3`

x = 3, y = 0

Use the following table to draw the graph.

x	0	3
y	2	0

Draw the graph by plotting the two points A(0, 2) and B(3, 0) from table

Graph of the equation   .....(ii)

4x + 6y = 12 ......(ii)

Putting x = 0 in equation (ii) we get

`=> 4 xx 0 + 6y = 12`

`=> y = 2`

x = 0, y = 2

Puting y = 0 in equation (ii) we get

`=> 4x + 6 xx 0 = 12`

`=> x = 3`

x = 3, y = 0

Use the following table to draw the graph.

x	0	3
y	2	0

Draw the graph by plotting the two points C(0, 2), D(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.