1. **State the problem:** Solve the system of equations by substitution: $$y = -7x + 10$$ $$y = -10x + 16$$ 2. **Use substitution method:** Since both equations equal $y$, set the right sides equal to each other: $$-7x + 10 = -10x + 16$$ 3. **Solve for $x$:** Add $10x$ to both sides: $$-7x + 10 + 10x = -10x + 16 + 10x$$ $$3x + 10 = 16$$ Subtract 10 from both sides: $$3x + \cancel{10} - \cancel{10} = 16 - 10$$ $$3x = 6$$ Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{6}{\cancel{3}}$$ $$x = 2$$ 4. **Find $y$ by substituting $x=2$ into one of the original equations:** Using $y = -7x + 10$: $$y = -7(2) + 10 = -14 + 10 = -4$$ 5. **Final answer:** $$\boxed{(x, y) = (2, -4)}$$ This means the two lines intersect at the point $(2, -4)$.