question_answer

Find whether the following pair of linear equations is consistent or inconsistent:

\[3x+2y=8\]

\[6x-4y=9\]

Answer:

Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{3}{6}=\frac{1}{2},\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{2}{-4}=\frac{-1}{2}\]

\[\frac{1}{2}\ne \frac{-1}{2}\]

Since \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\], which will give a unique solution.

Hence, given pair of linear equations is consistent.