Check whether the given pair of linear equations satisfy the conditions of unique solution.
x−3y=2 and −2x+6y=5
⇒x−3y−2=0 and −2x+6y−5=0
Since, the pair of equations have a unique solution, if a1a2≠b1bx
⇒ Here, we have
a1=1,b1=−3,c1=−2
a2=−2,b2=6,c2=−5.
⇒a1a2=1−2=−12,b1b2=−36=−12
⇒a1a2=b1b2, which does not satisfy the condition of unique solution.
Hence, the two straight paths represented by the equartions x−3y=2 and −2x+6y=5 do not cross each other.