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

Putting in equation we get:

Putting in equationswe get:

Use the following table to draw the graph.

Draw the graph by plotting the two points from table

Graph of the equation….

Putting in equations we get:

Putting in equationwe get:

Use the following table to draw the graph.

Draw the graph by plotting the two points 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.