1. **State the problem:** We have a system of equations arranged in a grid with unknowns represented by question marks (?). The goal is to find the value of the unknowns. 2. **Write down the equations from the grid:** From the first row: $? + 9 + ... = 13$ From the second row: $7 + ... - 5 = 6$ From the third row: $... - ... + 8 = 12$ From the last row (equalities): $4, 7, 14$ 3. **Analyze the given equalities:** The last row shows sums for each column: - Column 1 sum: 4 - Column 2 sum: 7 - Column 3 sum: 14 4. **Use the column sums to find unknowns:** Let the unknowns be $x$, $y$, and $z$ corresponding to the question marks in the first row, second row, and third row respectively. 5. **From the first column sum:** The first column has $? + 7 + ... = 4$ Assuming the first column values are $x$, $7$, and some unknown $a$, then: $$x + 7 + a = 4$$ 6. **From the second column sum:** Second column has $9 + ... - ... = 7$ Assuming the second column values are $9$, $b$, and $c$, then: $$9 + b - c = 7$$ 7. **From the third column sum:** Third column has $... - 5 + 8 = 14$ Assuming the third column values are $d$, $-5$, and $8$, then: $$d - 5 + 8 = 14$$ Simplify: $$d + 3 = 14$$ $$d = 11$$ 8. **Use the row equations:** - First row: $x + 9 + y = 13$ - Second row: $7 + b - 5 = 6$ Simplify second row: $$7 + b - 5 = 6 \\ 2 + b = 6 \\ b = 4$$ - Third row: $c - a + 8 = 12$ Simplify: $$c - a = 4$$ 9. **Use column sums to find $a$ and $c$:** From step 5: $$x + 7 + a = 4 \\ a = 4 - x - 7 = -3 - x$$ From step 6: $$9 + b - c = 7 \\ 9 + 4 - c = 7 \\ 13 - c = 7 \\ c = 6$$ 10. **Use $c - a = 4$ from step 8:** $$6 - a = 4 \\ a = 2$$ 11. **From $a = -3 - x$ and $a = 2$:** $$2 = -3 - x \\ x = -5$$ 12. **Use first row equation to find $y$:** $$x + 9 + y = 13 \\ -5 + 9 + y = 13 \\ 4 + y = 13 \\ y = 9$$ **Final answer:** The unknown $?$ corresponds to $x = -5$.