Easy Maths Brain Teasers | Algebra Problems - Free Printable

Yes, we can solve this puzzle! Let’s break it down step by step.

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We are given a 2x2 grid with variables A, B, C, D and the following equations:

```
A + B = 13
C + D = 4
A - C = 3
B + D = 8
```

We need to find the values of A, B, C, and D that satisfy all four equations.

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Step 1: Write down the system of equations

1. A + B = 13
2. C + D = 4
3. A - C = 3
4. B + D = 8

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Step 2: Solve using substitution or elimination

Let’s use equation (3) to express A in terms of C:

> From (3): A = C + 3

Now plug this into equation (1):

> (C + 3) + B = 13
> → B = 13 - C - 3
> → B = 10 - C

Now plug B = 10 - C into equation (4):

> (10 - C) + D = 8
> → D = 8 - 10 + C
> → D = C - 2

Now plug this expression for D into equation (2):

> C + D = 4
> → C + (C - 2) = 4
> → 2C - 2 = 4
> → 2C = 6
> → C = 3

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Step 3: Back-substitute to find other variables

- C = 3
- From (3): A = C + 3 → A = 6
- From earlier: B = 10 - C → B = 7
- From earlier: D = C - 2 → D = 1

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Step 4: Verify all equations

1. A + B = 6 + 7 = 13 ✔
2. C + D = 3 + 1 = 4 ✔
3. A - C = 6 - 3 = 3 ✔
4. B + D = 7 + 1 = 8 ✔

All equations are satisfied!

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✔ Final Answer:

- A = 6
- B = 7
- C = 3
- D = 1

This is the unique solution to the puzzle.