`{:(0.04x + 0.02y = 5),(0.5(x - 2) - 0.4y = 29):}`

Answer

To solve the given system of equations:

1. **Write the equations:**
\[ 0.04x + 0.02y = 5 \quad \text{(Equation 1)} \]
\[ 0.5(x - 2) - 0.4y = 29 \quad \text{(Equation 2)} \]

2. **Multiply Equation 1 by 100 to eliminate decimals:**
\[ 100(0.04x + 0.02y) = 100 \cdot 5 \]
This simplifies to:
\[ 4x + 2y = 500 \quad \text{(Equation 3)} \]

3. **Multiply Equation 2 by 10 to eliminate decimals:**
\[ 10(0.5(x - 2) - 0.4y) = 10 \cdot 29 \]
This simplifies to:
\[ 5(x - 2) - 4y = 290 \]
Expanding this gives:
\[ 5x - 10 - 4y = 290 \]
Rearranging it, we get:
\[ 5x - 4y = 300 \quad \text{(Equation 4)} \]

4. **Now we have two equations:**
\[ 4x + 2y = 500 \quad \text{(Equation 3)} \]
\[ 5x - 4y = 300 \quad \text{(Equation 4)} \]

5. **Multiply Equation 4 by 2 to align the coefficients of \(y\):**
\[ 2(5x - 4y) = 2 \cdot 300 \]
This simplifies to:
\[ 10x - 8y = 600 \quad \text{(Equation 5)} \]

6. **Now we have:**
\[ 4x + 2y = 500 \quad \text{(Equation 3)} \]
\[ 10x - 8y = 600 \quad \text{(Equation 5)} \]

7. **Next, we can multiply Equation 3 by 4 to align the coefficients of \(y\):**
\[ 4(4x + 2y) = 4 \cdot 500 \]
This simplifies to:
\[ 16x + 8y = 2000 \quad \text{(Equation 6)} \]

8. **Now we add Equation 5 and Equation 6:**
\[ (10x - 8y) + (16x + 8y) = 600 + 2000 \]
This simplifies to:
\[ 26x = 2600 \]
Dividing both sides by 26 gives:
\[ x = 100 \]

9. **Substituting \(x = 100\) back into Equation 3 to find \(y\):**
\[ 4(100) + 2y = 500 \]
This simplifies to:
\[ 400 + 2y = 500 \]
Rearranging gives:
\[ 2y = 500 - 400 \]
\[ 2y = 100 \]
Dividing both sides by 2 gives:
\[ y = 50 \]

10. **Final solution:**
\[ x = 100, \quad y = 50 \]