1. The problem is to rewrite the equation $ax + by = c$ given that $y = \frac{1}{5}x - 4$. 2. We start by substituting the expression for $y$ into the original equation: $$ax + b\left(\frac{1}{5}x - 4\right) = c$$ 3. Distribute $b$ over the terms inside the parentheses: $$ax + \frac{b}{5}x - 4b = c$$ 4. Combine like terms involving $x$: $$\left(a + \frac{b}{5}\right)x - 4b = c$$ 5. To isolate $x$, add $4b$ to both sides: $$\left(a + \frac{b}{5}\right)x = c + 4b$$ 6. Finally, solve for $x$ by dividing both sides by $\left(a + \frac{b}{5}\right)$: $$x = \frac{c + 4b}{a + \frac{b}{5}}$$ This expresses $x$ in terms of $a$, $b$, and $c$ given the original equation and the expression for $y$. Alternatively, the rewritten form of the original equation after substitution is: $$ax + b\left(\frac{1}{5}x - 4\right) = c$$