Solve the following equations by graphical method- x + y = 4

2x – 3y = 3

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

We have the equations,

x + y = 4 …(i)

2x – 3y = 3 …(ii)

Take equation (i), we have

x + y = 4

We can write it as,

x = (4 – y) …(iii)

Now, assign values of y and compute values for 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 = 4 – 0

⇒ x = 4

We have, (4, 0).

Now, put y = 1.

Then, x = 4 – 1

⇒ x = 3

We have, (3, 1).

Now, put y = 2.

Then, x = 4 – 2

⇒ x = 2

We have, (2, 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 = 3

We can write it as,

2x = 3y + 3

…(iv)

Assign values for y and compute x.

For equation (iv):

Say, we put y = 0.

Then,

⇒ x = 1.5

We have, (1.5, 0).

Now, put y = 1.

Then,

⇒ x = 3

We have, (3, 1).

Now, put y = 2.

Then,

⇒ x = 3 × 2

⇒ x = 6

We have, (6, 2).

Record it in a table,

Represent the two tables on a graph, we get

Notice the intersection point of these two lines, x + y = 4 and 2x – 3y = 3.

These two lines intersect each other at (3, 1).

⇒ (3, 1) is the solution of these equations.

Thus, solution is x = 3 and y = 1.