Question

For all real values of c, the pair of equations x – 2y = 8, 5x – 10y = c have a unique solution. Justify whether it is true or false.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

The given pair of linear equations

x – 2y – 8 = 0

5x – 10y = c

Here, a₁ = 1, b₁ = – 2, c₁ = a – 8

a₂ = 5, b₂ = – 10, c₂ = – c

Now, `a_1/a_2 = 1/5, b_1/b_2 = (-2)/(-10) = 1/5`

`c_1/c_2 = (-8)/(-c) = 8/c`

But if c = 40 (real value),

Then the ratio `c_1/c_2` becomes `1/5` and then the system of linear equations has an infinitely many solutions.

Hence, ate = 40, the system of linear equations does not have a unique solution.