The given system of equations is:

1. $2a - 3b = 4$
2. $a + 3b = 20$

Let's solve this system of linear equations.

Step 1: Solve the second equation for $a$:

$a = 20 - 3b$

Step 2: Substitute $a = 20 - 3b$ into the first equation:

$2(20 - 3b) - 3b = 4$ $40 - 6b - 3b = 4$ $40 - 9b = 4$ $-9b = 4 - 40$ $-9b = -36$ $b = 4$

Step 3: Substitute $b = 4$ into $a = 20 - 3b$:

$a = 20 - 3(4)$ $a = 20 - 12$ $a = 8$

Final Solution:

$a = 8, \, b = 4$

Would you like a step-by-step explanation, or do you have further questions?

Here are 5 related questions:

1. What methods can be used to solve systems of equations other than substitution?
2. Can these equations be solved graphically, and what would the solution represent?
3. How would the solution change if one of the coefficients were altered?
4. What is the determinant of the system matrix for these equations?
5. How do we verify the solution to the system of equations?

Tip: Always check your solution by substituting the values back into the original equations.