Answer:
To solve for x and y, we can use algebraic manipulation and substitution. Here are the steps:
Rearrange the first equation to solve for y in terms of x:
y = 2 - x
Substitute this expression for y into the second equation, and simplify:
x^3 + (2-x)^3 = 56
x^3 + 8 - 12x + 6x^2 - 3x^3 = 56
-2x^3 + 6x^2 - 12x + 8 = 0
Divide both sides by -2 to simplify the equation:
x^3 - 3x^2 + 6x - 4 = 0
Try to find a root of the equation using synthetic division or guess and check. One possible root is x = 2. Substituting this back into the first equation gives:
2 + y = 2
y = 0
So the solution is x=2 and y=0.
Therefore, the solution to the system of equations is x = 2 and y = 0.