Question

Which of the following system of equations has no solution?

• A. $3x-y=2,9x-3y=6$
• B. $4x-7y+28=0,5y-7x+9=0$
• C. $3x-5y-11=0,6x-10y-7=0$
• D. None of these

Answer 1

Answer: (C)

$3x-5y-11=0,6x-10y-7=0$

For a system of equations $a_{1}x+b_{1}y+c_1=0;a_{2}x+b_{2}y+c_2=0$ to have no solution, the condition to be satisfied is

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Checking the condition on all the options :

Option A

$\frac{3}{9}=\frac{-1}{-3}=\frac{2}{6}$

All these fractions when simplified give $\frac{1}{3}$, hence the system of equations has solutions.

Option B

$\frac{4}{-7}\ne \frac{-7}{5}=\frac{28}{9}$

All these fractions are unequal, hence the system of equations has solutions.

Option C

$\frac{3}{6}=\frac{-5}{-10}\ne \frac{-11}{-7}$

All these fractions satisfy the required condition, hence the system of equations has no solutions.