Q22 of 186 Page 3

For what value of a, the following system of linear equations has no solutions:
ax + 3y = a – 2, 12x + ay = a

Given, pair of equations

ax + 3y = a – 2

and 12x + ay = a

On comparing the given equation with standard form i.e. a₁ x + b₁y + c₁ = 0 and a₂ x + b₂y + c₂ = 0, we get

a₁ = a, b₁ = 3 and c₁ = – (a – 2)

and a_{2 =} 12, b₂ = a and c₂ = – a

For no solutions,

∴

On taking I and II terms, we get

⇒ a² = 36

⇒ a = √36

⇒ a = ±6

Find the values of a and b for which the following system of linear equations has infinitely many solutions:

(a – 1) x + 3y = 2, 6x + (1 – 2b) y = 6

Find the values of a and b for which the following system of linear equations has infinitely many solutions:

2x + 3y = 7, (a + b + 1) x + (a + 2b + 2) y = 4 (a + b) + 1

For what value of a, the following system of linear equations has no solutions:

x + 2y = 5, 3x + ay + 15 = 0

For what value of a, the following system of linear equations has no solutions:

3x + y = 1, (2a – 1) x + (a – 1) y = 2a + 1

For what value of a, the following system of linear equations has no solutions:ax + 3y = a – 2, 12x + ay = a