1. **State the problem:** Solve the system of equations: $$y = 5x$$ $$y - x^2 = 5x - 9$$ 2. **Substitute** the expression for $y$ from the first equation into the second equation: $$5x - x^2 = 5x - 9$$ 3. **Simplify** the equation by subtracting $5x$ from both sides: $$\cancel{5x} - x^2 - \cancel{5x} = \cancel{5x} - 9 - \cancel{5x}$$ $$-x^2 = -9$$ 4. **Multiply both sides by $-1$** to make the quadratic term positive: $$x^2 = 9$$ 5. **Solve for $x$** by taking the square root of both sides: $$x = \pm 3$$ 6. **Find corresponding $y$ values** using $y = 5x$: - For $x = 3$, $y = 5 \times 3 = 15$ - For $x = -3$, $y = 5 \times (-3) = -15$ 7. **Solutions to the system** are: $$(3, 15) \text{ and } (-3, -15)$$ 8. **Check given points:** The points $(-8.91, -44.58)$ and $(-1, -5.47)$ do not satisfy the system exactly, so they are not solutions. **Final answer:** The exact solutions are $(3, 15)$ and $(-3, -15)$.