**Solution:**

To solve the given system of equations, we will use the substitution, elimination, and cross multiplication methods. Let's solve each equation one by one.

**Equation 1: 0.4x + 0.3y = 1.7**

To solve this equation using substitution method, we will isolate one variable and substitute it into the other equation.

Step 1: Solve for x in terms of y:

0.4x = 1.7 - 0.3y
x = (1.7 - 0.3y)/0.4

Now, we will substitute this value of x into the second equation.

**Equation 2: 0.7x - 0.2y = 0.8**

Substituting the value of x, we get:

0.7((1.7 - 0.3y)/0.4) - 0.2y = 0.8

Simplifying the equation:

0.7(1.7 - 0.3y) - 0.2y = 0.8(0.4)

0.7(1.7) - 0.7(0.3y) - 0.2y = 0.32

1.19 - 0.21y - 0.2y = 0.32

Combine like terms:

1.19 - 0.41y = 0.32

Subtracting 1.19 from both sides:

-0.41y = 0.32 - 1.19

-0.41y = -0.87

Dividing both sides by -0.41:

y = -0.87/(-0.41)
y = 2.121

Now, substitute this value of y back into Equation 1 to solve for x.

0.4x + 0.3(2.121) = 1.7

0.4x + 0.6363 = 1.7

0.4x = 1.7 - 0.6363

0.4x = 1.0637

Dividing both sides by 0.4:

x = 1.0637/0.4
x = 2.659

Therefore, the solution to the system of equations is x = 2.659 and y = 2.121.

**Equation 3: 7(y - 3) - 2(x + 2) = 14**

To solve this equation using elimination method, we will eliminate one variable by multiplying the equations by suitable coefficients so that the coefficients of one variable become equal.

Step 1: Distribute and simplify the equation:

7y - 21 - 2x - 4 = 14

7y - 2x - 25 = 14

Step 2: Rearrange the equation:

7y - 2x = 14 + 25

7y - 2x = 39

This equation can't be further simplified.

**Equation 4: 4(y - 2) + 3(x - 3) = 2**

To solve this equation using cross multiplication method, we will multiply both sides of the equation by the denominators of the fractions to eliminate the fractions.

Step 1