Solution:
Given equations are:
3x + 4y = 7 …(i)
4x + y = 3 …(ii)

To find the values of x and y, we can use any of the following methods:
Method 1: Substitution method

- Solve one of the equations for one variable in terms of the other variable.
- Substitute this expression into the other equation and solve for the remaining variable.
- Substitute the value of this variable into either of the original equations to find the value of the other variable.

Let's solve the given equations using substitution method:

From equation (ii), we have:
y = 3 - 4x …(iii)

Substituting equation (iii) in equation (i), we get:
3x + 4(3 - 4x) = 7
3x + 12 - 16x = 7
-13x = -5
x = 5/13

Substituting this value of x in equation (iii), we get:
y = 3 - 4(5/13)
y = 27/13

Hence, the solution of the given set of equations is (x, y) = (5/13, 27/13).

Method 2: Elimination method

- Multiply one or both of the equations by constants such that when the two equations are added or subtracted, one of the variables is eliminated.
- Solve for the remaining variable.
- Substitute the value of this variable into either of the original equations to find the value of the other variable.

Let's solve the given equations using elimination method:

Multiplying equation (ii) by 4, we get:
16x + 4y = 12 …(iv)

Subtracting equation (i) from equation (iv), we get:
13x = 5
x = 5/13

Substituting this value of x in equation (i), we get:
3(5/13) + 4y = 7
y = 27/13

Hence, the solution of the given set of equations is (x, y) = (5/13, 27/13).

Therefore, option (b) is the correct answer.