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For the given system of equation show graphically that equation has infinitely many solution: a-2b=5 3a-6b=15
Class 10 | 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: a-2b=5 3a-6b=15

Given,

a-2b=5……. (i)

3a-6b=15……. (ii)

For equation (i),

⇒ b=(a-5)/2

When a=3, we get b=(3-5)/2=-1

When a=5, we get b=(5-5)/2=0

Thus, we have the following table giving points on the line a-2b=5

a 3 5
b -1 0

For equation (ii),

Solve for b:

⇒ b=(3a-15)/6

So, when a=1

b=(3(1)-15)/6=-2

And, when a=-1

⇒ b=(3(-1)-15)/6=-3

Thus, we have the following table giving points on the line 3a-6b=15

a 1 -1
b -2 -3

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

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

i

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