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.
$5x-3y=11;-10x+6y=22$

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

Answer 1

Answer: (B)

Inconsistent

The given linear equation are
$\Rightarrow 5x-3y-11=\mathrm{0....}eq1$
$\Rightarrow a_1=5,b_1=-3,c_1=-11$
$\Rightarrow -10x+6y-22=\mathrm{0...}eq2$
$\Rightarrow a_2=-10,b_2=6,c_2=-22$
$\Rightarrow \frac{a_1}{a_2}=\frac{5}{-10}\Rightarrow -\frac{1}{2}$
$\Rightarrow \frac{b_1}{b_2}=\frac{-3}{6}\Rightarrow -\frac{1}{2}$
$\Rightarrow \frac{c_1}{c_2}=\frac{-11}{-22}\Rightarrow \frac{1}{2}$
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.