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 pair of linear equations is consistent or inconsistent: $5x-3y=11;\ -10x+6y=-22$

Given: Pair of equations: $5x-3y=11;\ -10x+6y=-22$

To do: To find out whether the given pair of equations is consistent or inconsistent.

Solution:

Given equations are: $5x-3y=11;\ -10x+6y=-22$

$\frac{a_1}{a_2}=\frac{5}{-10}=-\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{-3}{6}=-\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{11}{-22}=-\frac{1}{2}$

Here we find, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions.

Thus, the given pair of linear equations is consistent.
 

Updated on: 10-Oct-2022

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