1. **State the problem:** We are given two simultaneous linear equations: $$\text{(1) } 5e + f = 16$$ $$\text{(2) } e + f = 0$$ We want to solve for the variables $e$ and $f$ by eliminating one variable. 2. **Identify the elimination operation:** To eliminate a variable, we either add or subtract the equations so that one variable cancels out. 3. **Check the coefficients of $f$:** Both equations have $+f$, so subtracting the second equation from the first will eliminate $f$: $$ (5e + f) - (e + f) = 16 - 0 $$ 4. **Perform the subtraction:** $$ 5e + f - e - f = 16 $$ $$ (5e - e) + (f - f) = 16 $$ $$ 4e + \cancel{f} - \cancel{f} = 16 $$ $$ 4e = 16 $$ 5. **Solve for $e$:** $$ e = \frac{16}{4} = 4 $$ 6. **Substitute $e=4$ into equation (2) to find $f$:** $$ 4 + f = 0 $$ $$ f = -4 $$ **Final answer:** $$ e = 4, \quad f = -4 $$