Mathematics

Problem

3. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

and

\frac{c_{1}}{c_{2}}

, find out whether the following pair of linear equations are consistent, or inconsistent. (i)

3 x+2 y=5 ; \quad 2 x-3 y=7

(ii)

2 x-3 y=8 ; \quad 4 x-6 y=9

(iii)

\frac{3}{2} x+\frac{5}{3} y=7 ; 9 x-10 y=14

(iv)

5 x-3 y=11 ;-10 x+6 y=-22

(v)

\frac{4}{3} x+2 y=8 ; 2 x+3 y=12