Linear Equations with Two Variables: Applying the formula

Note that in the current system of equations, one of the variables is isolated alone on the left side of the equation:

$\begin{cases} \underline{x}+y=8 \\ \bm{x=\underline{5-y}} \\ \end{cases}$

Therefore, we can use the substitution method and substitute the entire expression that x equals in the second equation in place of x in the first equation (marked with an underline in both equations above) and thus we'll get one equation with one variable:

$\underline{ 5-y}+y=8$

where we highlight the equation in which the variable we substituted is isolated in order to return to it later after we find the value of y from solving the equation we got, and this is to find using it the value of x corresponding to that y value we found, therefore we highlighted this equation above.

From here - we'll continue and solve the single-variable equation we got,

First- we'll combine like terms on the left side of the resulting equation:

$5-y+y=8 \\ 5=8$$$

We'll stop here and notice that y cancelled out in the current equation and we got a false statement, this is because clearly:

$5\neq8$ meaning-

We got a false statement regardless of the variables' values,

We can conclude from here that the system of equations has no solution, because no matter which values we substitute for the variables - we won't get a true statement in both equations together.

Therefore the correct answer is answer D.