Chapter 3: Pair of Linear Equations in Two Variables

(D) Parallel

Explanation:

The given equations are,

6x-3y+10 = 0

dividing by 3

⇒ 2x-y+ 10/3= 0… (i)

And 2x-y+9=0…(ii)

Table for 2x-y+ 10/3 = 0,

Table for 2x-y+9=0

Hence, the pair of equations represents two parallel lines.

(D) no solution

Explanation:

The equations are:

x + 2y + 5 = 0

–3x – 6y + 1 = 0

a₁ = 1; b₁ = 2; c₁ = 5

a₂ = -3; b₂ = -6; c₂ = 1

a₁/a₂ = -1/3

b₁/b₂ = -2/6 = -1/3

c₁/c₂ = 5/1 = 5

Here,

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Therefore, the pair of equations has no solution.

(C) intersecting or coincident

Explanation:

Conditions for a pair of linear equations to be consistent are:

Intersecting lines, having a unique solution,

a₁/a₂ ≠ b₁/b₂

Coincident or dependent

a₁/a₂ = b₁/b₂ = c₁/c₂

(D) no solution

Explanation:

The given pair of equations are y = 0 and y = – 7.

Graphically, both lines are parallel and have no solution

(D) intersecting at (a, b)

Explanation:

Graphically in every condition,

a, b>>0

a, b< 0

a>0, b< 0

a<0, b>0 but a = b≠ 0.

The pair of equations x = a and y = b graphically represents lines which are intersecting

at (a, b).

Hence, in this case, two lines intersect at (a, b).