Question

find whether the line representing the following pairs of linear equations intersect at a point,are parallel or coincident:3/2x+5/3y=7 and 3/2x+2/3y=6​

Answer 1

these lines are intersecting

coz

$\frac{a1}{a2} \: is \: not \: equal \: to \frac{b1}{b2}$

if a1/a2 not equal to b1/b2, lines intersect at a point. this means that the equation has one common solution.

if a1/a2 equals b1/b2 not equal to c1/c2, lines are parallel to each other. this means that the equations have no common solution.

if a1/a2 equals b1/b2 equals c1/c2, lines are coincident. this means that the equations have infinite number of common solutions.