1. **State the problem:** Solve the system of equations by substitution: $$y = 2x - 3$$ $$y = -4x + 21$$ 2. **Use substitution:** Since both expressions equal $y$, set them equal to each other: $$2x - 3 = -4x + 21$$ 3. **Solve for $x$:** Add $4x$ to both sides: $$2x + \cancel{-3} + 4x = \cancel{-4x} + 21 + 4x$$ $$6x - 3 = 21$$ Add $3$ to both sides: $$6x - \cancel{3} + 3 = 21 + \cancel{3}$$ $$6x = 24$$ Divide both sides by $6$: $$\frac{6x}{\cancel{6}} = \frac{24}{\cancel{6}}$$ $$x = 4$$ 4. **Find $y$ by substituting $x=4$ into one of the original equations:** $$y = 2(4) - 3 = 8 - 3 = 5$$ 5. **Final solution:** $$\boxed{(x, y) = (4, 5)}$$ This means the two lines intersect at the point $(4,5)$.