Question

Find the number of solutions of the given pair of linear equations:

$3x-y=3,9x-3y=9$

• A. Infinitely many solutions
• B. No solution
• C. Ambiguous
• D. None of these

Answer 1

The correct option is A Infinitely many solutions

$3x-y=3$ and $9x-3y=9$

Hence, $a_1=3,b_1=-1$ and $a_2=9,b_2=-3$

$\therefore \frac{a_1}{a_2}=\frac{3}{9}=\frac{1}{3}$

And, $\frac{b_1}{b_2}=\frac{-1}{-3}=\frac{1}{3}$

Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}$

Therefore, the given pair of linear equations are inconsistent and has infinitely many solutions.