Question

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

$3x+5y=16;4x-y=6$

• A. No Solution
• B. Infinitely many solutions
• C. Unique solution
• D. Cannot be determined

Answer 1

The correct option is C Unique solution

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 a unique solution is -

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

We have $\frac{3}{4}\ne \frac{5}{-1}$

Hence, Unique Solution