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

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.


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