1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y = 5x + 7 \\ y = 4x - 3 \end{cases}$$ 2. **Use substitution:** Since both expressions equal $y$, set them equal to each other: $$5x + 7 = 4x - 3$$ 3. **Solve for $x$:** $$5x + 7 = 4x - 3$$ Subtract $4x$ from both sides: $$5x - \cancel{4x} + 7 = \cancel{4x} - 3$$ $$x + 7 = -3$$ Subtract 7 from both sides: $$x + \cancel{7} = -3 - \cancel{7}$$ $$x = -10$$ 4. **Find $y$ by substituting $x = -10$ into one of the original equations:** Using $y = 5x + 7$: $$y = 5(-10) + 7 = -50 + 7 = -43$$ 5. **Solution:** $$(x, y) = (-10, -43)$$ This is the point where the two lines intersect.