The first equation gives you an equation to express y in terms of x. So, in the second equation, we use that expression to, well, substitute y.
As a consequence, the second equation will be entirely written in terms of x, and thus solvable:
[tex]\begin{cases}y=x+9\\3x+8y=-5\end{cases}\implies 3x+8(x+9)=-5 \iff 3x+8x+72=-5[/tex]
Solving for x, we have
[tex]3x+8x+72=-5 \iff 11x = -77 \iff x=-\dfrac{77}{11}=-7[/tex]
Now that the value of x is known, we can solve for y using the substitution expression:
[tex]y=-7+9=2[/tex]
