Question

On comparing the ratios $\frac{a_1}{a_2},\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pairs of linear equations are consistent, or inconsistent.
$2x-3y=8;4x-6y=9$

• A. Consistent
• B. Inconsistent
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is B Inconsistent

The given linear equation are
$\Rightarrow 2x-3y-8=\mathrm{0....}eq1$
$\Rightarrow a_1=2,b_1=-3,c_1=-8$
$\Rightarrow 4x-6y-9=\mathrm{0...}eq2$
$\Rightarrow a_2=4,b_2=-6,c_2=-9$
$\Rightarrow \frac{a_1}{a_2}=\frac{2}{4}\Rightarrow \frac{1}{2}$
$\Rightarrow \frac{b_1}{b_2}=\frac{-3}{-6}\Rightarrow \frac{1}{2}$
$\Rightarrow \frac{c_1}{c_2}=\frac{-8}{-9}$
comparing
$\Rightarrow \frac{a_1}{a_2},\frac{b_1}{b_2},\frac{c_1}{c_2}$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Hence, the following pairs of linear equations are inconsistent.