The system of equations $7x+9y=15$ and $14x+18y=30$ has:

The equations are:$7x+9y=15$$14x+18y=30$ Divide the second equation by 2:
$$\frac{14x}{2}+\frac{18y}{2}=\frac{30}{2}$$
$$7x+9y=15$$
Both equations are identical. This represents the same line. Since all points on the line satisfy both equations, there are infinitely many solutions.Alternatively, check ratios: $\frac{a_1}{a_2}=\frac{7}{14}=\frac{1}{2}$, $\frac{b_1}{b_2}=\frac{9}{18}=\frac{1}{2}$, $\frac{c_1}{c_2}=\frac{15}{30}=\frac{1}{2}$.Since $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, there are infinitely many solutions.