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.
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