`{:(0.4x + 0.3y = 1.7),(0.7x - 0.2y = 0.8):}`

Answer

To solve the system of equations:

1. **Equations**:
\[ 0.4x + 0.3y = 1.7 \quad \text{(1)} \]
\[ 0.7x - 0.2y = 0.8 \quad \text{(2)} \]

2. **Multiply both equations by 10** to eliminate the decimals:
\[ 4x + 3y = 17 \quad \text{(3)} \]
\[ 7x - 2y = 8 \quad \text{(4)} \]

3. **Rearrange equation (4)** to express \(x\) in terms of \(y\):
\[ 7x = 8 + 2y \]
\[ x = \frac{8 + 2y}{7} \quad \text{(5)} \]

4. **Substitute equation (5)** into equation (3):
\[ 4\left(\frac{8 + 2y}{7}\right) + 3y = 17 \]

5. **Multiply through by 7** to eliminate the fraction:
\[ 4(8 + 2y) + 21y = 119 \]
\[ 32 + 8y + 21y = 119 \]
\[ 32 + 29y = 119 \]

6. **Isolate \(y\)**:
\[ 29y = 119 - 32 \]
\[ 29y = 87 \]
\[ y = \frac{87}{29} = 3 \]

7. **Substitute \(y = 3\)** back into equation (5) to find \(x\):
\[ x = \frac{8 + 2(3)}{7} \]
\[ x = \frac{8 + 6}{7} \]
\[ x = \frac{14}{7} = 2 \]

8. **Final solution**:
\[ x = 2, \quad y = 3 \]