Final answer:
The simplified expressions are 8x + 6y for part (a) and 4x + 2y for part (b), obtained by combining like terms and ensuring all similar variables are added or subtracted appropriately.
Step-by-step explanation:
To simplify the algebraic expressions given in parts (a) and (b), we should combine like terms by adding or subtracting the coefficients of the terms that have the same variable.
Part (a): 5x + 3x + 2y + 4y
Combine the x terms:
5x + 3x = 8x
Combine the y terms:
2y + 4y = 6y
So the simplified expression for part (a) is:
8x + 6y
Part (b): 6x - 2x + 8y - 6y
Combine the x terms:
6x - 2x = 4x
Combine the y terms:
8y - 6y = 2y
So the simplified expression for part (b) is:
4x + 2y
To check if the answers are reasonable, we confirm that all like terms have been combined and that there are no further simplifications possible. In both cases, the answers are indeed reasonable.