Question

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

Options

• a unique solution

• exactly two solutions

• infinitely many solutions

• no solution

Answer 1

The pair of linear equations x + 2y + 5 = 0 and – 3x – 6y + 1 = 0 has no solution.

Explanation:

Given that,

x + 2y + 5 = 0

and – 3x – 6y + 1 = 0

We have, `a_1/a_2 = 1/-3 = -1/3`

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

`\implies c_1/c_2 = 5/1`

So, `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Hence, there is no solution for these pair of linear equations.