Solution

The equations are
$$\Rightarrow 2x+3y-5=0$$
here, $$ a_{1}=2,b_{1}=3,c_{1}=-5$$

$$\Rightarrow 6x+9y-15=0$$
here, $$ a_{2}=6,b_{2}=9,c_{2}=-15$$

$$\Rightarrow \displaystyle \frac{a_{1}}{a_{2}}=\frac{2}{6}= \frac{1}{3} $$

$$\Rightarrow \displaystyle \frac{b_{1}}{b_{2}}=\frac{3}{9}=\frac{1}{3}$$

$$\Rightarrow \displaystyle \frac{c_{1}}{c_{2}}=\frac{-5}{-15}=\frac{1}{3}$$

$$\Rightarrow \displaystyle \frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}=\frac{c_{1}}{c_{2}}$$

Hence, the given system of equations has an infinite number of solutions.