Question

The pair of linear equations $x+2y=5,3x+12y=10$ has

• A. Unique solution
• B. No solution
• C. More than two solutions
• D. Infinitely many solutions

Answer 1

The correct option is A Unique solution

Given equations are:
$x+2y=5$
$3x+12y=10$
From the equations we have:
$\Rightarrow a_1=1,b_1=2$
$\Rightarrow a_2=3,b_2=12$
$\frac{a_1}{a_2}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{2}{12}=\frac{1}{6}$
$\Rightarrow \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
Hence system of equations has a unique solution