1. **State the problem:** Convert the inequality system to an equation system using slack variables and write the associated linear equation. 2. **Given inequality:** $$3x_1 + 7x_2 \leq 21$$ with constraints $$x_1, x_2 \geq 0$$. 3. **Slack variable introduction:** To convert the inequality to an equation, introduce slack variable $$s_1 \geq 0$$ such that $$3x_1 + 7x_2 + s_1 = 21$$. 4. **Interpretation:** The slack variable $$s_1$$ represents the unused portion of the resource, ensuring the equation holds exactly. 5. **Basic variables table:** Possible basic variables are $$x_1, x_2, s_1$$. 6. **Feasibility:** Since $$x_1, x_2, s_1 \geq 0$$ and the equation is balanced, the system is feasible for values satisfying the equation and nonnegativity. **Final associated linear equation:** $$3x_1 + 7x_2 + s_1 = 21$$