Question

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

x − 2y = 5

3x − 6y = 15

Answer 1

The given equations are

x - 2y = 5 ....(i)

3x - 6y = 15 .....(ii)

Putting x = 0 in equation (i) we get

=> 0 - 2y = 5

=> y = -5/2

Putting y = 0 in equation (i) we get

`=> x - 2xx0 = 5`

`=> x = 5`

x = 5,  y = 0

x	0	5
y	-5/2	0

Draw the graph by plotting the two points A(0, -5/2) and B(5,0) from table

Graph of the equation ...(ii)

3x - 6y = 15 ...(ii)

Putting x = 0 in equation (ii) we get

`=> 3 xx 0 - 6y = 15`

=> y = -5/2

x = 0, y = -5/2

Putting y = 0 in equation (ii) we get

`=> 3x - 6xx 0 = 15`

`=> x = 5`

x = 5, y = 0

Use the following table to draw the graph.

x	0	5
y	-5/2	0

Draw the graph by plotting the two points C(0, -5/2) and D(5,0) 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.