1. **Problem statement:** Solve the system of equations: $$3x - 2y = 11$$ $$4x + 5y = 7$$ 2. **Method:** Use the elimination method by multiplying each equation to align coefficients for elimination. 3. Multiply the first equation by 5: $$5(3x - 2y) = 5(11) \Rightarrow 15x - 10y = 55$$ 4. Multiply the second equation by 2: $$2(4x + 5y) = 2(7) \Rightarrow 8x + 10y = 14$$ 5. Add the two new equations to eliminate $y$: $$ (15x - 10y) + (8x + 10y) = 55 + 14 $$ $$ 15x + 8x = 69 $$ $$ 23x = 69 $$ 6. Solve for $x$: $$ x = \frac{69}{23} = 3 $$ 7. Substitute $x=3$ into the first original equation to find $y$: $$ 3(3) - 2y = 11 $$ $$ 9 - 2y = 11 $$ $$ -2y = 11 - 9 = 2 $$ $$ y = \frac{-2}{2} = -1 $$ **Final answer:** $$ x = 3, \quad y = -1 $$ This matches your method and result, so your understanding is correct!