1. The problem is to solve the system of equations: $$5x + 7y = 8$$ $$-2x - 7y = -20$$ 2. Sofia used the elimination method, which involves adding or subtracting equations to eliminate one variable. 3. Adding the two equations: $$5x + 7y + (-2x - 7y) = 8 + (-20)$$ $$5x - 2x + 7y - 7y = 8 - 20$$ $$3x + \cancel{0} = -12$$ $$3x = -12$$ 4. Solving for $x$: $$x = \frac{-12}{3}$$ $$x = -4$$ 5. Substitute $x = -4$ into the first equation: $$5(-4) + 7y = 8$$ $$-20 + 7y = 8$$ 6. Solve for $y$: $$7y = 8 + 20$$ $$7y = 28$$ $$y = \frac{28}{7}$$ $$y = 4$$ 7. Sofia's solution is $x = -4$, $y = -4$ but the correct $y$ value is $4$. 8. The mistake first occurred in section B where she wrote $7y = -28$ instead of $7y = 28$. Final answer: Sofia's mistake first occurred in section B.