1. **State the problem:** Solve the system of equations by elimination: $$10x + 2y = 18$$ $$10x - 7y = -18$$ 2. **Write the system:** Equation 1: $10x + 2y = 18$ Equation 2: $10x - 7y = -18$ 3. **Eliminate $x$ by subtracting Equation 2 from Equation 1:** $$ (10x + 2y) - (10x - 7y) = 18 - (-18) $$ $$ 10x + 2y - 10x + 7y = 18 + 18 $$ $$ 9y = 36 $$ 4. **Solve for $y$:** $$ y = \frac{36}{9} $$ $$ y = 4 $$ 5. **Substitute $y=4$ into Equation 1 to find $x$:** $$ 10x + 2(4) = 18 $$ $$ 10x + 8 = 18 $$ $$ 10x = 18 - 8 $$ $$ 10x = 10 $$ 6. **Solve for $x$:** $$ x = \frac{10}{10} $$ $$ x = 1 $$ 7. **Final solution:** $$ (x, y) = (1, 4) $$