Question:
If a pair of linear equations is consistent, then the lines will be
(a) parallel
(b) always coincident
(c) intersecting or coincident
(d) always intersecting
Solution:
(c) Condition for a consistent pair of linear equations
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ [intersecting lines having unique solution]
and $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ [coincident or dependent]
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