On comparing the ratios  $a_1,\ a_2,\ b_1,\ b_2$ and  $c_1,\ c_2$, find out whether the following pairs of linear equations are consistent, or inconsistent. $23x+35y=7;\ 9x-10y=14$.

Given: Pairs of linear equations: $23x+35y=7;\ 9x-10y=14$.

To do: To find out whether the following pairs of linear equations are consistent, or inconsistent by comparing the ratios  $a_1,\ a_2,\ b_1,\ b_2$ and  $c_1,\ c_2$.

Solution:

Here, $a_1=23,\ b_1=35,\ c_1=7$ and $a_2=9,\ b_2=-10,\ c_2=14$
 

Therefore, 

$\frac{a_1}{a_2}=\frac{23}{9}$

$\frac{b_1}{b_2}=\frac{35}{10}=\frac{7}{2}$

Here, $\frac{a_1}{a_2}≠\frac{b_1}{b_2}$

Therefore, The given pair of equations have a unique solution.

Thus, the given pair of equations is consistent.

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Updated on: 10-Oct-2022

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