System Substitution Cbcda2

1. **State the problem:** Solve the system of equations by substitution: $$y = -9x + 5$$ $$y = -10x$$ 2. **Use substitution method:** Since both expressions equal $y$, set them equal to each other: $$-9x + 5 = -10x$$ 3. **Solve for $x$:** Add $10x$ to both sides: $$-9x + 10x + 5 = -10x + 10x$$ $$x + 5 = 0$$ Subtract $5$ from both sides: $$x + \cancel{5} - \cancel{5} = 0 - 5$$ $$x = -5$$ 4. **Find $y$ by substituting $x = -5$ into one of the original equations:** Using $$y = -10x$$: $$y = -10(-5) = 50$$ 5. **Final solution:** $$x = -5, \quad y = 50$$ This means the system's solution is the point $(-5, 50)$ where both lines intersect.