Question

The system
x + ay=4
ax +9y=5
has the unique solution if a= ...​

Answer 1

I hope it would be helpful for you

Answer 2

The value of a ∈ R-{3, -3}.

The system ; x + ay = 4 and ax + 9y = 5 has the unique solution.

We have to find the value of a.

Concept : We know, If a pair of linear equations of two variables is given ;

i.e., a₁x + b₁y = c₁ and a₂x + b₂y = c₂

• for unique solution ⇒a₁/a₂ ≠ b₁/b₂
• for infinitely many solutions ⇒a₁/a₂ = b₁/b₂ = c₁/c₂
• for no solution ⇒a₁/a₂ = b₁/b₂

∴ for unique solution, a₁/a₂ ≠ b₁/b₂

here, a₁ = 1 , a₂ = a , b₁ = a and b₂ = 9

⇒1/a ≠ a/9

⇒a² ≠ 9

⇒(a² - 9) ≠ 0

⇒(a - 3)(a + 3) ≠ 0

⇒a ≠ 3 , -3

Therefore the value of a ∈ R-{3, -3}.