1. **State the problem:** Solve the simultaneous equations: $$3x - y = -4$$ $$2x - 3y = 9$$ 2. **Formula and method:** We will use the substitution or elimination method to solve these linear equations. Here, elimination is convenient. 3. **Elimination method:** Multiply the first equation by 3 to align the coefficients of $y$: $$3(3x - y) = 3(-4) \Rightarrow 9x - 3y = -12$$ 4. **Subtract the second equation from this new equation:** $$ (9x - 3y) - (2x - 3y) = -12 - 9 $$ $$ 9x - 3y - 2x + 3y = -21 $$ $$ 7x = -21 $$ 5. **Solve for $x$:** $$ x = \frac{-21}{7} = -3 $$ 6. **Substitute $x = -3$ into the first original equation:** $$ 3(-3) - y = -4 $$ $$ -9 - y = -4 $$ $$ -y = -4 + 9 $$ $$ -y = 5 $$ $$ y = -5 $$ 7. **Final answer:** $$ x = -3, \quad y = -5 $$ This means the solution to the system is the point $(-3, -5)$ where both equations intersect.