Solving Linear Equations Sudoku PDF Form - FormsPal - Free Printable

Problem Overview:

The task involves solving 27 linear equations and placing the solutions into a Sudoku-like grid. Each equation is labeled with a coordinate (e.g., AJ, AM, EO, etc.), and the solutions will be used to fill in the corresponding cells in the grid. After solving all equations, the remaining boxes in the grid must be filled using Sudoku rules.

Step-by-Step Solution:

#### Equation Solutions:

1. AJ: \( -9 = x - 14 \)
\[
x = -9 + 14 = 5
\]
Solution: \( x = 5 \)

2. AM: \( -2x - 13 = -3x - 5 \)
\[
-2x + 3x = -5 + 13 \implies x = 8
\]
Solution: \( x = 8 \)

3. AO: \( 4x - 2x = 18 \)
\[
2x = 18 \implies x = 9
\]
Solution: \( x = 9 \)

4. AQ: \( 3m + 4.5m = 15 \)
\[
7.5m = 15 \implies m = \frac{15}{7.5} = 2
\]
Solution: \( m = 2 \)

5. AR: \( \frac{2w}{16} = \frac{30}{80} \)
\[
\frac{w}{8} = \frac{3}{8} \implies w = 3
\]
Solution: \( w = 3 \)

6. BJ: \( -4(x + 6) = -40 \)
\[
x + 6 = \frac{-40}{-4} = 10 \implies x = 10 - 6 = 4
\]
Solution: \( x = 4 \)

7. BO: \( 7m - 3m - 6 = 6 \)
\[
4m - 6 = 6 \implies 4m = 12 \implies m = 3
\]
Solution: \( m = 3 \)

8. CL: \( \frac{2}{3} + \frac{3k}{4} = \frac{71}{12} \)
\[
\frac{3k}{4} = \frac{71}{12} - \frac{2}{3} = \frac{71}{12} - \frac{8}{12} = \frac{63}{12} = \frac{21}{4}
\]
\[
3k = 21 \implies k = 7
\]
Solution: \( k = 7 \)

9. CP: \( 8y - (2y - 3) = 9 \)
\[
8y - 2y + 3 = 9 \implies 6y + 3 = 9 \implies 6y = 6 \implies y = 1
\]
Solution: \( y = 1 \)

10. DJ: \( 4n - 7 = 5 - 2n \)
\[
4n + 2n = 5 + 7 \implies 6n = 12 \implies n = 2
\]
Solution: \( n = 2 \)

11. DK: \( \frac{2}{n} = \frac{14}{n + 30} \)
\[
2(n + 30) = 14n \implies 2n + 60 = 14n \implies 60 = 12n \implies n = 5
\]
Solution: \( n = 5 \)

12. DN: \( \frac{4}{6} = \frac{m}{9} \)
\[
\frac{2}{3} = \frac{m}{9} \implies m = \frac{2}{3} \times 9 = 6
\]
Solution: \( m = 6 \)

13. DR: \( 6(y + 3) = 24 \)
\[
y + 3 = \frac{24}{6} = 4 \implies y = 4 - 3 = 1
\]
Solution: \( y = 1 \)

14. EO: \( \frac{w + 1}{4} = \frac{25}{50} \)
\[
\frac{w + 1}{4} = \frac{1}{2} \implies w + 1 = 2 \implies w = 1
\]
Solution: \( w = 1 \)

15. FJ: \( 3x - 7 = 20 \)
\[
3x = 27 \implies x = 9
\]
Solution: \( x = 9 \)

16. FN: \( \frac{c}{5} - 4 = -3 \)
\[
\frac{c}{5} = 1 \implies c = 5
\]
Solution: \( c = 5 \)

17. FQ: \( 3x - 2 = 16 \)
\[
3x = 18 \implies x = 6
\]
Solution: \( x = 6 \)

18. FR: \( 9 = -4y + 6y - 5 \)
\[
9 = 2y - 5 \implies 2y = 14 \implies y = 7
\]
Solution: \( y = 7 \)

19. GL: \( -6x + 2x = -36 \)
\[
-4x = -36 \implies x = 9
\]
Solution: \( x = 9 \)

20. GP: \( 6 - 3(2k - 4) = -18 \)
\[
6 - 6k + 12 = -18 \implies 18 - 6k = -18 \implies -6k = -36 \implies k = 6
\]
Solution: \( k = 6 \)

21. HM: \( -0.04x + 1.32 = 1.08 \)
\[
-0.04x = 1.08 - 1.32 = -0.24 \implies x = \frac{-0.24}{-0.04} = 6
\]
Solution: \( x = 6 \)

22. HR: \( 4x - 3 = x + 9 \)
\[
4x - x = 9 + 3 \implies 3x = 12 \implies x = 4
\]
Solution: \( x = 4 \)

23. IJ: \( 4\left(\frac{1}{4} + y\right) = 5 \)
\[
1 + 4y = 5 \implies 4y = 4 \implies y = 1
\]
Solution: \( y = 1 \)

24. IK: \( 6x = 24 \)
\[
x = 4
\]
Solution: \( x = 4 \)

25. IM: \( 3x + 4 = x + 18 \)
\[
3x - x = 18 - 4 \implies 2x = 14 \implies x = 7
\]
Solution: \( x = 7 \)

26. IO: \( 0.5t - 3t + 5 = 0 \)
\[
-2.5t + 5 = 0 \implies -2.5t = -5 \implies t = 2
\]
Solution: \( t = 2 \)

27. IR: \( -(z + 5) = -14 \)
\[
z + 5 = 14 \implies z = 9
\]
Solution: \( z = 9 \)

Filling the Grid:

Using the solutions above, place each value in the corresponding cell of the grid. For example:
- AJ: \( x = 5 \) → Cell AJ gets 5
- AM: \( x = 8 \) → Cell AM gets 8
- AO: \( x = 9 \) → Cell AO gets 9
- And so on...

After filling in all 27 cells, use Sudoku rules to fill in the remaining empty cells. Ensure that each row, column, and 3x3 box contains the numbers 1 through 9 without repetition.

Final Answer:

\[
\boxed{\text{Solutions are provided above; use them to fill the grid and solve the Sudoku.}}
\]