1. **State the problem:** Find the y-value of the solution to the system of equations: $$y = 2x - 6$$ $$y = 5x - 21$$ This means we want the y-coordinate where the two lines intersect. 2. **Set the equations equal to find x:** Since both equal y, set them equal: $$2x - 6 = 5x - 21$$ 3. **Solve for x:** Subtract $2x$ from both sides: $$\cancel{2x} - 6 = 5x - \cancel{2x} - 21 \implies -6 = 3x - 21$$ Add 21 to both sides: $$-6 + 21 = 3x - 21 + 21 \implies 15 = 3x$$ Divide both sides by 3: $$\frac{15}{\cancel{3}} = \frac{3x}{\cancel{3}} \implies 5 = x$$ 4. **Find y by substituting $x=5$ into one of the original equations:** Using $y = 2x - 6$: $$y = 2(5) - 6 = 10 - 6 = 4$$ 5. **Answer:** The y-value of the solution is **4**. This means the two lines intersect at the point $(5,4)$.