` 0.4 x + 0.3 y = 1.7`,
` 0.7 x - 0.2 y = 0.8`

Explanation

To solve the given system of linear equations:

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

2. **Multiply to Eliminate Decimals:**
To simplify the calculations, we can multiply both equations by 10 to eliminate the decimals:
\[ 10(0.4x + 0.3y) = 10(1.7) \implies 4x + 3y = 17 \quad \text{(3)} \]
\[ 10(0.7x - 0.2y) = 10(0.8) \implies 7x - 2y = 8 \quad \text{(4)} \]

3. **Multiply Equations to Align Coefficients:**
Next, we will multiply equation (3) by 2 and equation (4) by 3 to align the coefficients of \(y\):
\[ 2(4x + 3y) = 2(17) \implies 8x + 6y = 34 \quad \text{(5)} \]
\[ 3(7x - 2y) = 3(8) \implies 21x - 6y = 24 \quad \text{(6)} \]

4. **Add the Two New Equations:**
Now, we can add equations (5) and (6):
\[ (8x + 6y) + (21x - 6y) = 34 + 24 \]
This simplifies to:
\[ 29x = 58 \]

5. **Solve for \(x\):**
Divide both sides by 29:
\[ x = \frac{58}{29} = 2 \]

6. **Substitute \(x\) Back to Find \(y\):**
Now, substitute \(x = 2\) back into one of the original equations. We can use equation (4):
\[ 7(2) - 2y = 8 \]
Simplifying gives:
\[ 14 - 2y = 8 \]
Rearranging gives:
\[ -2y = 8 - 14 \implies -2y = -6 \]
Dividing by -2:
\[ y = \frac{-6}{-2} = 3 \]

7. **Final Solution:**
The solution to the system of equations is:
\[ x = 2, \quad y = 3 \]