Determine, whether the following pair of linear equation is consistent  /inconsistent. $x-y=8;\ 3x-3y=16$

Given: Equations: $x-y=8;\ 3x-3y=16$.

To do: To determine, whether the given pair of linear equation is consistent  /inconsistent. 

Solution:

Given equations: $x-y=8;\ 3x-3y=16$.
 

Here, $a_1=1,\ b_1=-1,\ c_1=8$ and $a_2=3,\ b_2=-3,\ c_2=16$.

$\frac{a_1}{a_2}=\frac{1}{3}$

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

$\frac{c_1}{c_2}=\frac{8}{16}=\frac{1}{2}$

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

Thus, given pair of linear equations has no solution.

Therefore, given pair of linear equations is inconsistent.

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Updated on: 10-Oct-2022

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