Solve the following equations by graphical method-2x – 3y + 13 = 0

3x – 2y + 12 = 0

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

We have the equations,

2x – 3y + 13 = 0 …(i)

3x – 2y + 12 = 0 …(ii)

Take equation (i), we have

2x – 3y + 13 = 0

We can write it as,

2x – 3y = -13

⇒ 3y – 2x = 13

⇒ 3y = 2x + 13

…(iii)

Now, assign values of x and compute values for 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 = 4.33

We have, (0, 4.33).

Now, put x = 1.

Then,

⇒ y = 5

We have, (1, 5).

Now, put x = 2.

Then,

⇒ y = 5.67

We have, (2, 5.67).

Now, put x = -1.

Then,

⇒ y = 3.67

We have, (-1, 3.67).

Now, put x = -2.

Then,

⇒ y = 3

We have, (-2, 3).

Now, put x = -3,

Then,

⇒ y = 2.33

We have, (-3, 2.33).

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

Record it in a table,

Now, take equation (ii),

3x – 2y + 12 = 0

We can write it as,

3x – 2y = -12

⇒ 2y – 3x = 12

⇒ 2y = 3x + 12

Assign values for x and compute y.

Say, we put x = 0.

Then,

⇒ y = 6

We have, (0, 6).

Now, put x = 1.

Then,

⇒

⇒ y = 7.5

We have, (1, 7.5).

Now, put x = 2.

Then,

⇒ y = 9

We have, (2, 9).

Now, put x = -1.

Then,

⇒ y = 4.5

Now, put x = -2.

Then,

⇒ y = 3

Now, put x = -3.

Then,

⇒ y = 1.5

Record it in a table,

Represent the two tables on a graph, we get

Notice the intersection point of these two lines, 2x – 3y + 13 = 0 and 3x – 2y +12 = 0.

These two lines intersect each other at (-2, 3) in the 2^nd quadrant.

⇒ (-2, 3) is the. solution of these equations.

Thus, solution is x = -2 and y = 3.