Classify the following pair of lines as coincident, parallel or intersecting
$3 x - 2 y + 5 = 0$ & $2 x + y - 5 = 0$

Intersecting

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Parallel

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Coincident

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None of these

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Solution

The correct option is C Intersecting
Comparing the two lines with $a_{1} x + b y_{1} + c = 0$ and $a_{2} x + b y_{2} + c = 0,$
As $\frac{a_{1}}{a_{2}} = \frac{3}{2}, \frac{b_{1}}{b_{2}} = \frac{- 2}{1}$ and $\frac{c_{1}}{c_{2}} = - 1$
Hence $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Therefore lines are intersecting.

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Classify the following pair of lines as coincident, parallel or intersecting3x−2y+5=0 & 2x+y−5=0

The correct option is C IntersectingComparing the two lines with a1x+by1+c=0 and a2x+by2+c=0,As a1a2=32,b1b2=−21 and c1c2=−1Hence a1a2≠b1b2≠c1c2Therefore lines are intersecting.

Classify the following pair of lines as coincident, parallel or intersecting
$3 x - 2 y + 5 = 0$ & $2 x + y - 5 = 0$