On comparing the ratios a1/a2, b1/b2 and c1/c2, find out whether the following pair of linear equations are consistent, or inconsistent. (i) 3x+2y=5; 2x-3y=7 (ii) 2x-3y=8; 4x-6y=9 (iii) (3/2)x+(5/3)y=7; 9x-10y=14 (iv) 5x-3y=11; -10x+6y=-22 (v) (4/3)x+2y=8; 2x+3y=12

(i) a1/a2=3/2, b1/b2=2/-3, c1/c2=5/7 => a1/a2≠b1/b2≠c1/c2, the lines intersect and have an unique consistent solution
(ii) a1/a2=2/4=1/2, b1/b2=-3/-6=1/2, c1/c2=8/9 => a1/a2=b1/b2≠c1/c2, the lines are parallel and have no solutions, i.e. the equations are an inconsistent pair
(iii) a1/a2=(3/2)/9=1/6, b1/b2=(5/3)/-10=-1/6, c1/c2=7/14=1/2 => a1/a2≠b1/b2≠c1/c2, the lines intersect and have an unique consistent solution
(iv) a1/a2=5/-10=-1/2, b1/b2=-3/6=-1/2, c1/c2=11/-22=-1/2 => a1/a2=b1/b2=c1/c2, the lines are coincident and have infinitely many solutions. The equations form a consistent pair of equations
(v) a1/a2=(4/3)/2=2/3, b1/b2=2/3, c1/c2=8/12=2/3 => a1/a2=b1/b2=c1/c2, the lines are coincident and have infinitely many solutions. The equations form a consistent pair of equations.