On comparing the ratios  $a_1,\ a_2,\ b_1,\ b_2$ and $c_1, c_2$, find out whether the following pair of linear equations are consistent, or inconsistent:
$5x−3y=11; −10x+6y=−22$

Given: Equation: $5x−3y=11;  −10x+6y=−22$

To do: To find weather the given pair of linear equations are consistent, or inconsistent.

Solution:

$\frac{a_1}{a_2}=\frac{5}{-10}=-\frac{1}{2},\ \frac{b_1}{b_2}=\frac{-3}{6}=-\frac{1}{2}$ and $\frac{c_1}{c_2}=\frac{11}{-22}=-\frac{1}{2}$

Here we find $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=-\frac{1}{2}$

The lines are coincident and have infinitely many solutions. The equations form a consistent pair of equations.
 

Updated on: 10-Oct-2022

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