Question

By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

x – 2y = 6, 3x – 6y = 0

Answer 1

Given pair of equation is

x – 2y = 6  ......(i)

And 3x – 6y = 0   ......(ii)

On comparing with ax + by + c = 0, we get

a₁ = 1, b₁ = –2 and c₁ = –6   .....[From (i)]

a₂ = 3, b₂ = –6 and c₂ = 0  ......[From (ii)]

Here, `a_1/a_2 = 1/3`,

`b_1/b_2 = (-2)/(-6) = 1/3`

And `c_1/c_2 = (-6)/0`

∴ `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Hence, the lines represented by the given equations are parallel.

Therefore, it has no solution.

So, the given pair of lines is inconsistent.