Solve the following equations by graphical method-

x + 3y = 6

2x – 3y = 12

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

We have the equations,

x + 3y = 6 …(i)

2x – 3y = 12 …(ii)

Take equation (i), we have

x + 3y = 6

We can write it as,

x = 6 – 3y …(iii)

Now, assign values of y and compute values of 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 atleast three values.

For equation (iii):

Say, we put y = 0.

Then, x = 6 – 3(0)

⇒ x = 6 – 0

⇒ x = 6

We have, (6, 0).

Now, put y = 1.

Then, x = 6 – 3(1)

⇒ x = 6 – 3

⇒ x = 3

We have, (3, 1).

Now, put y = 2.

Then, x = 6 – 3(2)

⇒ x = 6 – 6

⇒ x = 0

We have, (0, 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),

2x – 3y = 12

We can write it as,

…(iv)

Assign values for y and compute x.

For equation (iv):

Say, we put y = 0.

Then,

⇒ x = 6

We have, (6, 0).

Now, put y = 1.

Then,

⇒ x = 7.5

We have, (7.5, 1).

Now, put y = 2.

Then,

⇒ x = 9

We have, (9, 2).

Record it in a table.

Represent the two tables on a graph, we get

Notice the intersection point of these two lines, x + 3y = 6 and 2x – 3y = 12.

These two lines intersect each other at (6, 0).

⇒ (6, 0) is the solution of these equations.

Thus, solution is x = 6 and y = 0.