Solve the following equations by graphical method-

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

We have the equations,

…(i)

…(ii)

Take equation (i), we have

We can write it as,

⇒ 4x + y = 10

⇒ y = 10 – 4x

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 = 10 – 4(0)

⇒ y = 10 – 0

⇒ y = 10

We have, (0, 10).

Now, put x = 1.

Then, y = 10 – 4(1)

⇒ y = 10 – 4

⇒ y = 6

We have, (1, 6).

Now, put x = 2.

Then, y = 10 – 4(2)

⇒ y = 10 – 8

⇒ y = 2

We have, (2, 2).

Now, put x = 3.

Then, y = 10 – 4(3)

⇒ y = 10 – 12

⇒ y = -2

We have, (3, -2).

Now, put x = 4.

Then, y = 10 – 4(4)

⇒ y = 10 – 16

⇒ y = -6

We have, (4, -6).

Now, put x = 5.

Then, y = 10 – 4(5)

⇒ y = 10 – 20

⇒ y = -10

We have, (5, -10).

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

Record it in a table,

Now, take equation (ii),

We can write it as,

Assign values for x and compute y.

Say, we put x = 0.

Then,

⇒ y = -4

We have, (0, -4).

Now, put x = 1.

Then,

⇒ y = -4.5

We have, (1, -4.5).

Now, put x = 2.

Then,

⇒ y = -5

We have, (2, -5).

Now, put x = 3.

Then,

⇒ y = -5.5

We have, (3, -5.5).

Now, put x = 4.

Then,

⇒ y = -6

We have, (4, -6).

Now, put x = 5.

Then,

⇒ y = -6.5

We have, (5, -6.5).

Record it in a table.

Represent the two tables on a graph, we get

Notice the intersection point of these two lines, and .

These two lines intersect each other at (4, -6) in the 4^th quadrant.

⇒ (4, -6) is the solution of these equations.

Thus, solution is x = 4 and y = -6.