solve equation algebraically, check all solutions
y=x squared - x
x+y=4
you mean, solve the system of equations...
from the second equation, we see that $\displaystyle y = 4 - x$, plug this into the first equation, we get
$\displaystyle 4 - x = x^2 - x$
now continue. solve for all the values of $\displaystyle x$ and then plug them into $\displaystyle y = 4 - x$ to find the corresponding values for $\displaystyle y$