First Row: 
a−b+c=15
Second Row:
g∗h+i=14
Third Row: 
j−k+l=9

First column: 
a/g-j=-5
Second column:
b-h+k=2
Third column: 
c−i+l=11

solve this math given that above and follow this given below

1.the missing values are the whole numbers between 1 and 9
2.each number is only used once
3.each row is a math equation
4.each column is a math equation
5.remember that multiplication and division are performed before addition and subtraction 


We now have two sets of equations: one set for rows and one set for columns. The constraints are the same (whole numbers between 1 and 9, each used only once), and we need to ensure that both the row and column equations hold true simultaneously.

### Row Equations:
1. \( a - b + c = 15 \)
2. \( g \times h + i = 14 \)
3. \( j - k + l = 9 \)

### Column Equations:
1. \( \frac{a}{g} - j = -5 \)
2. \( b - h + k = 2 \)
3. \( c - i + l = 11 \)

Given these constraints, we will use a trial-and-error approach with systematic checking to find a set of values that satisfy all the equations simultaneously.

Let me find the solution by checking permutations of the numbers.The solution that satisfies all the row and column equations is:

- \( a = 9 \), \( b = 1 \), \( c = 7 \)
- \( g = 3 \), \( h = 4 \), \( i = 2 \)
- \( j = 8 \), \( k = 5 \), \( l = 6 \)

### Verification:

#### Row Equations:
1. \( 9 - 1 + 7 = 15 \) ✔️
2. \( 3 \times 4 + 2 = 14 \) ✔️
3. \( 8 - 5 + 6 = 9 \) ✔️

#### Column Equations:
1. \( \frac{9}{3} - 8 = 3 - 8 = -5 \) ✔️
2. \( 1 - 4 + 5 = 2 \) ✔️
3. \( 7 - 2 + 6 = 11 \) ✔️

All equations hold true, and all numbers between 1 and 9 are used exactly once.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the solution change if one of the row or column equations were modified?
2. What happens if we expand the range of numbers beyond 1 to 9?
3. Can you find a different set of values that also satisfies all conditions?
4. How does the introduction of multiplication affect the complexity of solving such problems?
5. What techniques can help in solving more complex puzzles with similar constraints?

**Tip**: When faced with multiple equations, organizing your steps and verifying small parts of the problem as you go can prevent errors and make solving easier.

Explore the detailed solution to a system of equations with constraints, involving both addition and multiplication. Check how whole numbers between 1 and 9 are used exactly once to satisfy each row and column equation. Ideal for advanced high school students and math enthusiasts.

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