Question

Without actually solving the simultaneous equations given below, decide whether the system has unique solution, no solution or infinitely many solutions.

$3y=2-x;3x=6-9y$

• A. Infinite solutions
• B. unique solution
• C. no solution
• D. Cannot be determined

Answer 1

The correct option is A Infinite solutions

As we know the condition for the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ to have infinite solutions is

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

Here the given system of linear equations is

$x+3y-2=0;3x+9y-6=0\frac{1}{3}=\frac{3}{9}=\frac{-2}{-6};$

$\therefore$ The system has infinite number of solutions.