1. **State the problem:** Solve the system of equations: $$2x - y = 3 + 5x^2$$ $$3x = -3 - y$$ 2. **Rewrite the second equation to express $y$ in terms of $x$: ** $$3x = -3 - y \implies y = -3 - 3x$$ 3. **Substitute $y = -3 - 3x$ into the first equation:** $$2x - (-3 - 3x) = 3 + 5x^2$$ 4. **Simplify the left side:** $$2x + 3 + 3x = 3 + 5x^2$$ $$5x + 3 = 3 + 5x^2$$ 5. **Subtract 3 from both sides:** $$5x + \cancel{3} - \cancel{3} = \cancel{3} + 5x^2 - \cancel{3}$$ $$5x = 5x^2$$ 6. **Rewrite the equation:** $$5x^2 - 5x = 0$$ 7. **Factor out $5x$:** $$5x(x - 1) = 0$$ 8. **Set each factor equal to zero:** $$5x = 0 \implies x = 0$$ $$x - 1 = 0 \implies x = 1$$ 9. **Find corresponding $y$ values using $y = -3 - 3x$: ** For $x=0$: $$y = -3 - 3(0) = -3$$ For $x=1$: $$y = -3 - 3(1) = -3 - 3 = -6$$ 10. **Final solution:** $$\boxed{(0, -3) \text{ and } (1, -6)}$$ These are the points where both equations are satisfied simultaneously.