Question

The pair of equations $5x-15y=8$ and $3x-9y=\frac{24}{5}$ has

• A. One solution
• B. Two solutions
• C. Infinitely many solutions
• D. No solution

Answer 1

The correct option is C Infinitely many solutions

Given equations are:
$5x-15y=8$ .....(1)
$3x-9y=\frac{24}{5}$
$\Rightarrow 15x-45y=24$ .....(2)
From the equations (1) and (2), we have
$\frac{a_1}{a_2}=\frac{5}{15}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{15}{45}=\frac{1}{3}$
$\frac{c_1}{c_2}=\frac{8}{24}=\frac{1}{3}$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Hence pair of equation has infinitely many solutions.