On comparing the ratios  of $\frac{a_1}{a_2},\ \frac{b_1}{b_2}$  and $\frac{c_1}{c_2}$, find out whether the following pairs of linear equations are consistent, or inconsiste $\frac{4}{3}x+2y=8$; $2x+3y=12$.

Given: $\frac{4}{3}x+2y=8$; $2x+3y=12$

To do: To find out whether the following pairs of linear equations are consistent, or inconsistent.

Solution:

The equations are

$\Rightarrow \frac{4}{3}x+2y−8=0$

$\Rightarrow a_1=\frac{4}{3},\ b_1=2,\ c_1=−8$

$\Rightarrow 2x+3y−12=0$

$\Rightarrow a_2=2,\ b_2=3,\ c_2=−12$

$\Rightarrow$ On comparing $\frac{a_1}{a_2},\ \frac{b_2}{b_1},\ \frac{c_2}{c_1}$
​
$\Rightarrow \frac{3}{2},\ \frac{3}{2},\ \frac{3}{2}$
​
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
​
$\therefore$ System is consistent.
 

Updated on: 10-Oct-2022

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