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  • Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not

Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5.Check whether the paths cross each other or not

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Solution:
Equations are: x – 3y – 2 = 0
–2x + 6y – 5 = 0
Here    a1 = 1, b1 = –3, c1 = –2
a2 = –2, b2 = 6, c2 = –5

\frac{a_{1}}{a_{2}}= -\frac{1}{2},\frac{b_{1}}{b_{2}}= \frac{-3}{6}= -\frac{1}{2},\frac{c_{1}}{c_{2}}= \frac{-2}{-5}= \frac{2}{5}
As we know that two lines cross each other when \frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}} but here \frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}

Hence the paths do not cross each other.

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