Question

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

$3x-7y=15;6x=14y+10$

• A. unique solution
• B. No solution
• C. infinitely many solutions.
• D. Cannot be determined

Answer 1

The correct option is B No solution

$3x-7y=15\Rightarrow a_1=3,b_1=-7,c_1=15$
$6x-14y=10\Rightarrow a_2=6,b_2=-14,c_1=10$
$\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\frac{b_1}{b_2}=\frac{-7}{-14}=\frac{1}{2}$
$\frac{c_1}{c_2}=\frac{15}{10}=\frac{3}{2}$
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
The given system of linear equations is inconsistent
Therefore, the given systems of linear equations has no solution