1. **State the problem:** Olivia is solving the system of equations: $$6x - 2y = -4$$ $$y = 3x + 2$$ We need to determine how many solutions this system has. 2. **Substitute the expression for $y$ from the second equation into the first:** $$6x - 2(3x + 2) = -4$$ 3. **Expand and simplify:** $$6x - 6x - 4 = -4$$ 4. **Simplify further:** $$0x - 4 = -4$$ which simplifies to $$-4 = -4$$ 5. **Interpretation:** The equation $-4 = -4$ is always true, meaning the two equations represent the same line. 6. **Conclusion:** Since the equations represent the same line, there are infinitely many solutions (all points on the line satisfy both equations).