Question

Find whether the pair of equations $5x-8y+1=0,3x-\frac{24}{5}y+\frac{3}{5}=0$ has no solution, unique solution or infinitely many solutions

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

Answer 1

The correct option is A Infinitely many solutions

Given System of equations are:
$5x-8y+1=0$
$3x-\frac{24}{5}y+\frac{3}{5}=0$
From equation (2) will get
$15x-24y+3=0$
Now from equation (1) and (2) will have:
$\frac{a_1}{a_2}=\frac{5}{15},\frac{b_1}{b_2}=\frac{-8}{-24},\frac{c_1}{c_2}=\frac{1}{3}$
$\Rightarrow \frac{a_1}{a_2}=\frac{1}{3},\frac{b_1}{b_2}=\frac{1}{3},\frac{c_1}{c_2}=\frac{1}{3}$
Therefore, system of equations have Infinitely many solutions.