Solve the following equations by graphical method- 3x – y = 2; 6x -2y = 4

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

We have the equations,

3x – y = 2 …(i)

6x – 2y = 4 …(ii)

Take equation (i), we have

3x – y = 2

We can write it as,

y = 3x – 2 …(iii)

Now, assign values of x and compute y.

We can assign values of x = …, -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 x = 0.

Then, y = 3(0) – 2

⇒ y = 0 – 2

⇒ y = -2

We have, (0, -2).

Now, put x = 1.

Then, y = 3(1) – 2

⇒ y = 3 – 2

⇒ y = 1

We have, (1, 1).

Now, put x = 2.

Then, y = 3(2) – 2

⇒ y = 6 – 2

⇒ y = 4

We have, (2, 4).

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

Record it in a table,

Now, take equation (ii),

6x – 2y = 4

We can write it as,

2(3x – y) = 4

⇒ 3x – y = 2

⇒ y = 3x – 2 …(iv)

Compare equation (iii) and (iv), they are equal.

⇒ Equation (i) and (ii) are also equal.

The table would be same for the second equation, as the first equation.

Represent the two tables on a graph, we get

Notice that, the two lines overlap on each other. (means, these two lines have an intersection at each point of their overlapping)

Since these lines do not have any particular point of intersection, we can say it has infinitely many solutions.

Thus, there are infinite solutions to these set of equations.