Question

y = 0.25 x + 12 ;
y = m(x + 3)
In the above system of equations, for what value of constant m, will the system of equation have no solution?

• A. 1
• B. 0.75
• C. 0.25

Answer 1

The correct option is C 0.25

y = 0.25x + 12
And y = m(x + 3)
y = mx + 3m
For the system to have no solutions, we know the lines representing the equations should be parallel.
Ratio of coefficient of x = ratio of coefficients of $y\ne$ ratio of constants
[Ratio of Coefficient of y ]= [Ratio of Coefficient of x]
$\frac{1}{1}=\frac{0.25}{m}$
M = 0.25
Ratio of constants $=\frac{12}{3m}=\frac{12}{3\times 0.25}=16$
Clearly not equal to ratio of coefficients. Hence, C is the correct answer.