Solve for w
[tex]\begin{gathered} 2w=8 \\ \text{Divide both sides by }2 \\ \frac{2w}{2}=\frac{8}{2} \\ w=4 \end{gathered}[/tex]Solve for z
[tex]\begin{gathered} z=w+1 \\ \text{Using the solution for }w,\text{ substitute it to the current equation} \\ z=(4)+1 \\ z=5 \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} y=2z-3w \\ \text{Substitute the previous solution with }w=4,\text{ and }z=5 \\ y=2(5)-3(4) \\ y=10-12 \\ y=-2 \end{gathered}[/tex]Solve for x
[tex]\begin{gathered} 3x+2y-z+5w=20 \\ \text{Substitute the previous solutions for }y,w,\text{ and }z \\ 3x+2(-2)-(5)+5(4)=20 \\ 3x-4-5+20=20 \\ 3x-9+20=20 \\ 3x+11=20 \\ 3x=20-11 \\ 3x=9 \\ \frac{3x}{3}=\frac{9}{3} \\ x=3 \end{gathered}[/tex]Conclusion
[tex]\begin{gathered} \text{Therefore, the solution to the system is} \\ x=3,y=-2,w=4,z=5 \end{gathered}[/tex]