1. **State the problem:** Solve the system of linear equations: $$9x - 2y = -50$$ $$-3x + 7y = 4$$ 2. **Choose a method:** We will use the elimination method to solve for $x$ and $y$. 3. **Eliminate one variable:** Multiply the second equation by 3 to align coefficients of $x$: $$3(-3x + 7y) = 3(4)$$ $$-9x + 21y = 12$$ 4. **Add the two equations:** $$9x - 2y = -50$$ $$-9x + 21y = 12$$ Adding gives: $$\cancel{9x} - 2y + \cancel{-9x} + 21y = -50 + 12$$ $$19y = -38$$ 5. **Solve for $y$:** $$y = \frac{-38}{19} = -2$$ 6. **Substitute $y = -2$ into the first equation:** $$9x - 2(-2) = -50$$ $$9x + 4 = -50$$ 7. **Solve for $x$:** $$9x = -50 - 4$$ $$9x = -54$$ $$x = \frac{-54}{9} = -6$$ **Final answer:** $$x = -6, \quad y = -2$$