1. **State the problem:** Solve the system of equations: $$0 = 2x_2 - 2x_1 - 4$$ $$0 = -14 - 2x_2 - 3x_3$$ $$x_3 = x_1 + x_2$$ 2. **Rewrite the first equation:** $$0 = 2x_2 - 2x_1 - 4 \implies 2x_2 - 2x_1 = 4$$ Divide both sides by 2: $$\cancel{2}x_2 - \cancel{2}x_1 = \frac{4}{2} \implies x_2 - x_1 = 2$$ 3. **Express $x_2$ in terms of $x_1$:** $$x_2 = x_1 + 2$$ 4. **Substitute $x_3 = x_1 + x_2$ into the second equation:** $$0 = -14 - 2x_2 - 3x_3 = -14 - 2x_2 - 3(x_1 + x_2)$$ Expand: $$0 = -14 - 2x_2 - 3x_1 - 3x_2 = -14 - 3x_1 - 5x_2$$ 5. **Substitute $x_2 = x_1 + 2$ into the above:** $$0 = -14 - 3x_1 - 5(x_1 + 2) = -14 - 3x_1 - 5x_1 - 10 = -24 - 8x_1$$ 6. **Solve for $x_1$:** $$-24 - 8x_1 = 0 \implies -8x_1 = 24 \implies x_1 = \frac{24}{-8} = -3$$ 7. **Find $x_2$ using $x_2 = x_1 + 2$:** $$x_2 = -3 + 2 = -1$$ 8. **Find $x_3$ using $x_3 = x_1 + x_2$:** $$x_3 = -3 + (-1) = -4$$ **Final answer:** $$x_1 = -3, \quad x_2 = -1, \quad x_3 = -4$$