Question

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

 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Answer 1

2x − 2y − 2 = 0, 4x − 4y − 5 = 0

a₁ = 2, b₁ = -2, c₁ = -2, a₂ = 4, b₂ = - 4, c₂ = -5

= `(a_1)/(a_2)=2/4=1/2,`

= `(b_1)/(b_2) = (-2)/(-4)=1/2`

= `(c_1)/(c_2) = (-2)/(-5)=2/5`

Since `(a_1)/(a_2)=(b_1)/(b_2) != (c_1)/(c_2)`

So, lines are parallel.

∴ The pair of linear equations are inconsistent.