1. **State the problem:** Solve the system of linear equations: $$7x + 3y = 3$$ $$3x - y = 7$$ Find the values of $x$ and $y$. 2. **Use substitution or elimination method:** Here, we use substitution. From the second equation: $$3x - y = 7 \implies y = 3x - 7$$ 3. **Substitute $y$ into the first equation:** $$7x + 3(3x - 7) = 3$$ 4. **Simplify:** $$7x + 9x - 21 = 3$$ $$16x - 21 = 3$$ 5. **Isolate $x$:** $$16x = 3 + 21$$ $$16x = 24$$ 6. **Divide both sides by 16:** $$x = \frac{24}{16}$$ $$x = \frac{\cancel{24}^{3} \times 8}{\cancel{16}^{2} \times 8} = \frac{3}{2}$$ 7. **Find $y$ using $y = 3x - 7$:** $$y = 3 \times \frac{3}{2} - 7 = \frac{9}{2} - 7 = \frac{9}{2} - \frac{14}{2} = -\frac{5}{2}$$ **Final answer:** $$x = \frac{3}{2}, \quad y = -\frac{5}{2}$$