Solve the following equations using graphical method: a+b=3 2a+5b=12
Solve the following equations using graphical method: a+b=3 2a+5b=12

Solution:

Given,

a+b=3……. (i)

2a+5b=12……. (ii)

From equation (i),

When we Put b=0, we get, a=3

When we Put a=0, we get, b=3

Thus, we have the following table giving Points on the line a+b=3

From equation (ii),

Solve for b:

b=(12-2a)/5

So, when we Put, a=1 we get value of b-

b=(12-2(1))/5=2

And, when a=6

b=(12-2(6))/5=0

Thus, we have the following table giving Points on the line 2a+5b=12

a 1 6
b 2 0

Graph of the equations (i) and (ii) is as below:

From the given graph, we can see that the two lines intersect at Point P(1,2)

Therefore, a=1 and b=2