To find the best approximation of the solution to the system of equations, we can use the substitution method.
First, we can solve the equation 3x + 5y = 24 for one variable. Let's solve for x:
3x = 24 - 5y
x = (24 - 5y)/3
Now we can substitute this expression for x into the other equation:
x = (24 - 5y)/3
-2 = (24 - 5y)/3
Now we can solve for y:
-6 = 24 - 5y
-5y = -30
y = 6
Now that we have the value of y, we can substitute it back into the expression for x:
x = (24 - 5*6)/3
x = (24 - 30)/3
x = -6/3
x = -2
So, the solution to the system of equations is (-2, 6). Therefore, the best approximation of the solution to the nearest integer values is (-2, 6).
