1. **State the problem:** Solve the system of equations using elimination: $$4x - 7y = 3$$ $$x - 7y = -15$$ 2. **Explain the elimination method:** The goal is to eliminate one variable by adding or subtracting the equations. Here, both equations have the term $-7y$, so subtracting one from the other will eliminate $y$. 3. **Subtract the second equation from the first:** $$ (4x - 7y) - (x - 7y) = 3 - (-15) $$ Simplify the left side: $$4x - 7y - x + 7y = 3 + 15$$ $$ (4x - x) + (-7y + 7y) = 18 $$ $$3x + 0 = 18$$ 4. **Solve for $x$:** $$3x = 18$$ $$x = \frac{18}{3} = 6$$ 5. **Substitute $x=6$ into one of the original equations to find $y$:** Using the second equation: $$6 - 7y = -15$$ 6. **Solve for $y$:** $$-7y = -15 - 6$$ $$-7y = -21$$ $$y = \frac{-21}{-7} = 3$$ 7. **Write the solution as an ordered pair:** $$(x, y) = (6, 3)$$ **Final answer:** The solution to the system is $(6, 3)$.