Question

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have ______.

Options

• A unique solution

• Exactly two solutions

• Infinitely many solutions

• No solution

Answer 1

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have 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

`a_1/a_2 = -1/3`

`b_1/b_2 = -2/6 = -1/3`

`c_1/c_2 = 5/1` = 5

Here,

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Therefore, the pair of equation has no solution.