Question

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

$\frac{x}{2}+\frac{y}{3}=4;\frac{x}{4}+\frac{y}{6}=2$

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

Answer 1

The correct option is B 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 gine system of linear equations is

$\frac{x}{2}+\frac{y}{3}-4=0;\frac{x}{4}+\frac{y}{6}-2=0$

We have $\frac{4}{2}=\frac{6}{3}=\frac{-4}{-2}$

Hence, the system has infinite no. of solutions.