1. **State the problem:** We want to convert the inequalities of the linear programming problem into equations by adding slack variables. 2. **Given inequalities:** $$7x_1 + 6x_2 \leq 13$$ $$8x_1 + 2x_2 \leq 9$$ 3. **Slack variables:** Slack variables $s_1$ and $s_2$ are added to convert inequalities into equalities. Slack variables represent unused resources and must be non-negative. 4. **First constraint with slack variable $s_1$:** $$7x_1 + 6x_2 + s_1 = 13$$ 5. **Second constraint with slack variable $s_2$:** Add $s_2$ to the second inequality: $$8x_1 + 2x_2 + s_2 = 9$$ 6. **Non-negativity constraints:** $$x_1, x_2, s_1, s_2 \geq 0$$ **Final system of equations:** $$\begin{cases} 7x_1 + 6x_2 + s_1 = 13 \\ 8x_1 + 2x_2 + s_2 = 9 \\ x_1, x_2, s_1, s_2 \geq 0 \end{cases}$$