Question

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

x – y = 8, 3x – 3y = 16

Answer 1

x - y = 8, 3x - 3y = 16

x - y - 8 = 0 and 3x - 3y - 16 = 0

∴ a₁ = 1, b₁ = -1, c₁ = -8

a₂ = 3, b₂ = -3, c₂ = -16

`a_1/a_2 = 1/3, b_1/b_2 = (-1)/-3 = 1/3 and c_1/c_2 = 8/16 = 1/2`

Since `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

So, lines are parallel.

∴ The pair of linear equations are inconsistent.