Solve the following equations by graphical method-

2x + y = 6

2x –y + 2= 0

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

We have the equations,

2x + y = 6 …(i)

2x – y + 2 = 0 …(ii)

Take equation (i), we have

2x + y = 6

We can write it as,

y = (6 – 2x) …(iii)

Now, assign values of x and compute values 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 = 6 – 2(0)

⇒ y = 6 – 0

⇒ y = 6

We have, (0, 6).

Now, put x = 1.

Then, y = 6 – 2(1)

⇒ y = 6 – 2

⇒ y = 4

We have, (1, 4).

Now, put x = 2.

Then, y = 6 – 2(2)

⇒ y = 6 – 4

⇒ y = 2

We have, (2, 2).

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),

2x – y + 2 = 0

We can write it as,

y = 2x + 2 …(iv)

Assign values for x and compute it y.

For equation (iv):

Say, we put x = 0.

Then, y = 2(0) + 2

⇒ y = 0 + 2

⇒ y = 2

We have, (0, 2).

Now, put x = 1.

Then, y = 2(1) + 2

⇒ y = 2 + 2

⇒ y = 4

We have, (1, 4).

Now, put x = 2.

Then, y = 2(2) + 2

⇒ y = 4 + 2

⇒ y = 6

We have, (2, 6).

Record it in a table.

Represent the two tables on a graph, we get

Notice the intersection point of these two lines, 2x + y = 6 and 2x – y + 2 = 0.

These two lines intersect each other at (1, 4).

⇒ (1, 4) is the solution of these equations.

Thus, solution is x = 1 and y = 4.