Question

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

$8y=x-10;2x=3y+7$

• A. Unique solution
• B. infinitely many solutions.
• C. no solution
• D. cannot be determined

Answer 1

The correct option is A 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 -

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

Here the given system of linear equation is

$x-8y=10;2x-3y=7$

we have $\frac{1}{2}\ne \frac{-8}{-3};$

$\therefore$ Unique Solution