Question

How many solutions does the given system of equations has/have?

$3x+4y=7$
$15x+20y=35$

• A. A unique solution
• B. Infinitely many solutions
• C. No solution
• D. None of the above

Answer 1

The correct option is B Infinitely many solutions

For a given pair of equations,

$a_{1}x+b_{1}y=c_1$
$a_{2}x+b_{2}y=c_2$

$\text{If}\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2},$
then, the system of equations have infinitely many solutions.

Here,
$\frac{3}{15}=\frac{4}{20}=\frac{7}{35}$

So, the system of equations have infinitely many solutions.