Solve the following equations by graphical method- 2x + 3y=8; 4x – 3/2y = 1

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

We have the equations,

2x + 3y = 8 …(i)

…(ii)

Take equation (i), we have

2x + 3y = 8

We can write it as,

⇒ 3y = 8 – 2x

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 atleast three values.

Say, we put x = 0.

Then,

⇒ y = 2.67

We have, (0, 2.67).

Now, put x = 1.

Then,

⇒ y = 2

We have, (1, 2).

Now, put x = 2.

Then,

⇒ y = 1.33

We have, (2, 1.33).

Now, put x = 3.

Then,

⇒ y = 0.67

We have, (3, 0.67).

We can further find out y by putting values of x = …,-5,-4,-3,…,6,7,… but here we have just put four values.

Record it in a table,

Now, take equation (ii),

We can write it as,

…(iv)

Assign values for x and compute it y.

For equation (iv):

Say, we put x = 0.

Then,

⇒ y = -0.67

We have, (0, -0.67).

Now, put x = 1.

Then,

⇒ y = 2

We have, (1, 2).

Now, put x = 2.

Then,

⇒ y = 4.67

We have, (2, 4.67).

Now, put x = 3.

Then,

⇒ y = 7.33

We have, (3, 7.33).

Record it in a table.

Represent the two tables on a graph, we get

Notice the intersection point of these two lines, 2x + 3y = 8 and .

These two lines intersect each other at (1, 2) in the 1^st quadrant.

⇒ (1, 2) is the solution of these equations.

Thus, solution is x = 1 and y = 2.