For all real values of c , the pair of equations `x - 2y = 8` and `5x - 10y = c` have no solution. Justify whether it is true of false .

Options

A. true
B. false
C. can not say anything
D. none of these

Answer

B

Explanation

False, the given pair of linear equations
x - 2y - 8 = 0
and `" " 5x - 10y - c = 0`
Here, `" " a_(1) = 1, b_(1) = -2, c_(1) = -8`
`" " a_(2) = 5, b_(2) = -10, c_(2) = -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, at c = 40, the system of linear equations does not have a unique solution.