Solve the following equations by graphical method- x – 2y = 6

3x – 6y = 0

For solving these equations by the graphical method, we need to form separate tables for each equation.

We have the equations,

x – 2y = 6 …(i)

3x – 6y = 0 …(ii)

Take equation (i), we have

x – 2y = 6

We can write it as,

x = (2y + 6) …(iii)

Now, assign values of y and compute values x.

We can assign values of y = …, -3, -2, -1, 0, 1, 2, 3, 4,…

It is not necessary to put all values. But to form an accurate graph, it is necessary to put at least three values.

For equation (iii):

Say, we put y = 0.

Then, x = 2(0) + 6

⇒ x = 0 + 6

⇒ x = 6

We have, (6, 0).

Now, put y = 1.

Then, x = 2(1) + 6

⇒ x = 2 + 6

⇒ x = 8

We have, (8, 1).

Now, put y = 2.

Then, x = 2(2) + 6

⇒ x = 4 + 6

⇒ x = 10

We have, (10, 2).

We can further find out x by putting values of y = 3, 4, 5,… but here we have just put three values.

Record it in a table,

Now, take equation (ii),

3x – 6y = 0

We can write it as,

3x = 6y

⇒ x = 2y …(iv)

Assign values for y and compute it for x.

For equation (iv):

Say, we put y = 0.

Then, x = 2(0)

⇒ x = 0

We have, (0, 0).

Now, put y = 1.

Then, x = 2(1)

⇒ x = 2

We have, (2, 1).

Now, put y = 2.

Then, x = 2(2)

⇒ x = 4

We have, (4, 2).

Record it in a table.

Represent the two tables on a graph, we get

Notice that, the two lines are parallel to each other. (means, these two lines will never meet each other)

If these lines will never intersect, then it won’t have any solution.

Thus, there are no solutions to these set of equations.