If $\frac{x}{y}=\frac{4}{5}$ and $7x+6y=29$, find the value of $y$.

Given:
$$\frac{x}{y}=\frac{4}{5}⟹x=\frac{4}{5}y$$

Substitute the value of $x$ in the given linear equation $7x+6y=29$:

$$7\left(\frac{4}{5}y\right)+6y=29$$

$$\frac{28y}{5}+6y=29$$

Take the LCM:

$$\frac{28y+30y}{5}=29$$

$$\frac{58y}{5}=29$$

$$58y=29\times 5$$

$$58y=145⟹y=\frac{145}{58}=2.5$$