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For the given system of equation show graphically that equation has infinitely many solution: 3a+b=8 6a+2b=16
CBSE | Exercise 3.2 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
For the given system of equation show graphically that equation has infinitely many solution: 3a+b=8 6a+2b=16

Given,

3a+b=8……. (i)

6a+2b=16……. (ii)

From equation (i),

⇒ b=(8-3a)

When a=2, we get b=(8-3(2))=2

When a=3, we get b=(8-3(3))=-1

Thus, we have the following table giving points on the line 3a+b=8

a 2 3
b 2 -1

From equation (ii),

Solve for b:

⇒ b=(16-6a)/2

So, when a=3

b=(16-6(3))/2=-1

And, when a=1

⇒ b=(16-6(1))/2=5

Thus, we have the following table giving points on the line 6a+2b=16

a 3 1
b -1 5

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

Thus, the from given graph of the two equations are coincident. Hence, the system of equations has infinitely many solutions.

i

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