On comparing the ratios $\frac{a_1}{a_2},\ \frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pairs of linear equations are consistent, or inconsistent: $2x-3y=8;\ 4x-6y=9$
Given: Pair of equations: $2x-3y=8;\ 4x-6y=9$
To do: To find out whether the given pair of equations is consistent or inconsistent.
Solution:
Given equations are: $2x-3y=8;\ 4x-6y=9$
$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}$
$\frac{c_1}{c_2}=\frac{8}{9}$
Here we find, $\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$
Therefore, these linear equations are parallel to each other and thus have no possible solution.
Thus, the pair of linear equations is inconsistent.
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