Solve the system of equations: { p - 3q = 5, 3p + 2q = 4

The system of equations is:

• p - 3q = 5
• 3p + 2q = 4

Step-by-step solution:

1. Step 1: Multiply the first equation by 3 to make the coefficients of 'p' the same.
   3 * (p - 3q) = 3 * 5
   3p - 9q = 15
2. Step 2: Now we have two equations with the same 'p' coefficient:
   3p - 9q = 15
   3p + 2q = 4
3. Step 3: Subtract the second equation from the modified first equation to eliminate 'p'.
   (3p - 9q) - (3p + 2q) = 15 - 4
   3p - 9q - 3p - 2q = 11
   -11q = 11
4. Step 4: Solve for 'q'.
   q = 11 / -11
   q = -1
5. Step 5: Substitute the value of 'q' (-1) back into the original first equation (p - 3q = 5) to solve for 'p'.
   p - 3(-1) = 5
   p + 3 = 5
6. Step 6: Solve for 'p'.
   p = 5 - 3
   p = 2

Answer: p = 2, q = -1