1. **State the problem:** Solve the system of equations: $$5x - 4y = -91$$ $$2x + 3y = 5$$ 2. **Mai's approach:** She isolates $x$ in the second equation: $$2x + 3y = 5 \implies x = 2.5 - 1.5y$$ 3. **Substitute $x$ into the first equation:** $$5(2.5 - 1.5y) - 4y = -91$$ Simplify: $$12.5 - 7.5y - 4y = -91$$ Combine like terms: $$12.5 - 11.5y = -91$$ 4. **Isolate $y$:** Subtract 12.5 from both sides: $$-11.5y = -91 - 12.5$$ $$-11.5y = -103.5$$ Divide both sides by $-11.5$: $$y = \frac{-103.5}{-11.5} = \cancel{\frac{-103.5}{-11.5}}\Rightarrow y = 9$$ 5. **Check Mai's value:** Mai found $y = -9$, but our calculation shows $y = 9$. So Mai made a sign error. 6. **Find $x$ using correct $y=9$:** $$x = 2.5 - 1.5(9) = 2.5 - 13.5 = -11$$ 7. **Verify solution $(x,y) = (-11, 9)$ in both equations:** First equation: $$5(-11) - 4(9) = -55 - 36 = -91$$ (True) Second equation: $$2(-11) + 3(9) = -22 + 27 = 5$$ (True) 8. **Conclusion:** Mai's solution $(16, -9)$ is incorrect due to a sign error in solving for $y$. The correct solution is $(-11, 9)$. 9. **Graphing:** Graphing the lines $5x - 4y = -91$ and $2x + 3y = 5$ will show they intersect at $(-11, 9)$, confirming the solution.