The answer is False.
The given pair of linear equations
x - 2y - 8 = 0
and 5x - 10y - c = 0
On Comparing with ax + by + c = 0;
Here,
Here, a1 = 1, b1 = - 2, c1 = - 8;
And a2 = 5, b2 = - 10, c2 = - c;
a1 /a2 = 1/5
b1 /b2 = 1/5
c1 /c2 = 8/c
But if c = 40 (real value), then the ratio c1/c2 becomes 1/5 and then the system of linear equations has an infinitely many solutions.
Hence, at c = 40, the system of linear equations does not have a unique solution.