Question

Question 5
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.

Answer 1

False, the given pair of linear equations
X – 2y – 8 = 0
and 5x – 10y – c = 0
$here,a_1=1b_1=-2c_1=-8a_2=5,b_2=-10,c_2=-cnow,\frac{a_1}{a_2}=\frac{1}{5}=\frac{b_1}{b_2}=\frac{-2}{-10}=\frac{1}{5}\frac{c_1}{c_2}=\frac{-8}{-c}=\frac{8}{c}$
But if c = 40 (real value), then the ratio $\frac{c_1}{c_2}$ becomes $\frac{1}{5}$ and then the system of linear equation has an infinitely many solutions
Hence, at c = 40, the system of linear equations does not have a unique solution.