1. **Stating the problem:** Solve the system of linear equations number 3: $$\begin{cases} x + 3y = -7 \\ -x + 2y = -8 \end{cases}$$ 2. **Formula and rules:** To solve a system of linear equations, we can use the addition (elimination) method or substitution method. Here, we use elimination by adding the two equations to eliminate $x$. 3. **Add the two equations:** $$ (x + 3y) + (-x + 2y) = -7 + (-8) $$ $$ \cancel{x} + 3y - \cancel{x} + 2y = -15 $$ $$ 5y = -15 $$ 4. **Solve for $y$:** $$ y = \frac{-15}{5} = -3 $$ 5. **Substitute $y = -3$ into the first equation:** $$ x + 3(-3) = -7 $$ $$ x - 9 = -7 $$ $$ x = -7 + 9 = 2 $$ 6. **Solution:** The solution to the system is $$ (x, y) = (2, -3) $$ 7. **Verification:** Substitute into the second equation: $$ -x + 2y = -8 $$ $$ -(2) + 2(-3) = -2 - 6 = -8 $$ This confirms the solution is correct.