Solve the following equations by graphical method-3x-4y=1;

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

We have the equations,

3x – 4y = 1 …(i)

…(ii)

Take equation (i), we have

3x – 4y = 1

We can write it as,

3x = 4y + 1

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 atleast three values.

Say, we put y = -3.

Then,

⇒ x = -3.67

We have, (-3.67, -3).

Now, put y = -2.

Then,

⇒ x = -2.33

We have, (-2.33, -2).

Now, put y = -1.

Then,

⇒ x = -0.33

We have, (-0.33, -1).

Now, put y = 0.

Then,

⇒ x = 0.33

We have, (0.33, 0).

Now, put y = 1.

Then,

⇒ x = 1.67

We have, (1.67, 1).

Now, put y = 2.

Then,

⇒ x = 3

We have, (3, 2).

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

Record it in a table,

Now, take equation (ii),

We can write it as,

⇒ -6x + 8y = 15

⇒ 6x = 8y – 15

Assign values for y and compute x.

Say, we put y = -3.

Then,

⇒ x = -6.5

We have, (-6.5, -3).

Now, put y = -2.

Then,

⇒ x = -5.167

We have, (-5.167, -2).

Now, put y = -1.

Then,

⇒ x = -3.83

We have, (-3.83, -1).

Now, put y = 0.

Then,

⇒ x = -2.5

We have, (-2.5, 0).

Now, put y = 1.

Then,

⇒ x = -1.167

We have, (-1.167, 1).

Now, put y = 2.

Then,

⇒ x = 0.167

We have, (0.167, 2).

Record it in a table,

Represent the two tables on a graph, we get

Notice that, the two lines are inconsistent. It mean that they will meet at a specific point and the point that we did not took in the solution.

That point will be (17/12, 13/16) and can be found that both the lines will intersect at this point.

So point (17/12, 13/16) is the solution to the given equations.