Question

Determine whether the following system of linear equations have no solution, infinitely many solution or unique solutions.

$x+2y=3,2x+4y=15$

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

Answer 1

The correct option is A No solution

The equations are
$\Rightarrow x+2y-3=0$
$\Rightarrow a_1=1,b_1=2,c_1=-3$
$\Rightarrow 2x+4y-15=0$
$\Rightarrow a_2=2,b_2=4,c_2=-15$
$\Rightarrow \frac{a_1}{a_2}=\frac{1}{2}$
$\Rightarrow \frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}$
$\Rightarrow \frac{a_1}{b_1}=\frac{a_2}{b_2}\ne \frac{c_1}{c_2}$
Hence, the given system of equations has no solution