1. **State the problem:** Solve the system by substitution: $$y = 7x - 22$$ $$7x - 3y = 10$$ 2. **Use substitution:** Substitute $y$ from the first equation into the second: $$7x - 3(7x - 22) = 10$$ 3. **Simplify inside the parentheses:** $$7x - 3 \times 7x + 3 \times 22 = 10$$ $$7x - 21x + 66 = 10$$ 4. **Combine like terms:** $$-14x + 66 = 10$$ 5. **Isolate $x$:** $$-14x = 10 - 66$$ $$-14x = -56$$ 6. **Divide both sides by $-14$:** $$x = \frac{-56}{-14}$$ $$x = 4$$ 7. **Substitute $x=4$ back into the first equation to find $y$:** $$y = 7(4) - 22$$ $$y = 28 - 22$$ $$y = 6$$ 8. **Final answer:** $$\boxed{(4, 6)}$$ Note: The problem states a circle around solution (4, 50) but substitution yields $y=6$. The correct solution by substitution is $(4,6)$.