To solve the system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation, x - 3y = 4, for x:
x = 3y + 4
Now we can substitute this value of x into the first equation, 3x + 2y = -21:
3(3y + 4) + 2y = -21
Simplifying this equation gives us:
9y + 12 + 2y = -21
Combining like terms, we have:
11y + 12 = -21
Subtracting 12 from both sides:
11y = -33
Dividing both sides by 11:
y = -3
Now, we can substitute this value of y back into x = 3y + 4:
x = 3(-3) + 4
Simplifying gives us:
x = -9 + 4
x = -5
Therefore, the solution to the system of equations 3x + 2y = -21 and x - 3y = 4 is x = -5 and y = -3.