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Determine the equations a-2b=2, 4a-2b=5 is consistent or in-consistent using graphical method
CBSE | Class 10 | Exercise 3.2 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
Determine the equations a-2b=2, 4a-2b=5 is consistent or in-consistent using graphical method

Given,

a-2b=2……. (i)

4a-2b=5……. (ii)

For equation (i),

⇒ b=(a-2)/2

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

When a=0, we have b=(0-2)/2=-1

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

a 2 0
b 0 -1

From equation (ii),

We solve for a:

⇒ a=(5+2b)/4

So, when b=0

a=(5+2(0))/4=5/4

And, when b=1.5

⇒ a=(5+2(1))/4=7/4

Thus, we have the following table giving points on the line 4a-2b=5

a 5/4 7/4
b 0 1

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

From graph, it can be seen that the two lines intersect at (1,0).

Hence, the system of equations is consistent.

i

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