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

2x + y - 6 = 0, 4x - 2y - 4 = 0

Given,

Equations :

⇒ 2x + y - 6 = 0, 4x - 2y - 4 = 0

Comparing equations 2x + y - 6 = 0 and 4x - 2y - 4 = 0 with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 respectively, we get :

a₁ = 2, b₁ = 1, c₁ = -6, a₂ = 4, b₂ = -2 and c₂ = -4.

$\dfrac{a$1}{a2} = \dfrac{2}{4} = \dfrac{1}{2}

$\dfrac{b$1}{b2} = \dfrac{1}{-2} = -\dfrac{1}{2}

Since, $\dfrac{a$1}{a2} ≠ $\dfrac{b$1}{b2}.

Hence, pair of lines are consistent.

1st equation : 2x + y - 6 = 0

⇒ y = 6 - 2x ……….(1)

2nd equation : 4x - 2y - 4 = 0

⇒ 2y = 4x - 4

⇒ 2y = 2(2x - 2)

⇒ y = 2x - 2 ………(2)

Table of values of equation (1),

Table of values of equation (2),

Steps of construction :

1. Plot the points (2, 2), (3, 0) and (4, -2) and join them to form equation (1).

2. Plot the points (0, -2), (1, 0) and (2, 2) and join them to form equation (2).

3. The lines intersect at A(2, 2), which is the required solution.

Hence, above pair of equations has a unique solution i.e. x = 2 and y = 2.