Question

Solve this system with four equations.3x + 2y - Z + 5w = 20y = 2z - 3wZ=w+12w = 8-

Answer 1

`\begin{gathered} \text{Given} \\ 3x+2y-z+5w=20 \\ y=2z-3w \\ z=w+1 \\ 2w=8 \end{gathered}`

Solve for w

`\begin{gathered} 2w=8 \\ \text{Divide both sides by }2 \\ (2w)/(2)=(8)/(2) \\ w=4 \end{gathered}`

Solve for z

`\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}`

Solve for y

`\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}`

Solve for x

`\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 \\ (3x)/(3)=(9)/(3) \\ x=3 \end{gathered}`

Conclusion

`\begin{gathered} \text{Therefore, the solution to the system is} \\ x=3,y=-2,w=4,z=5 \end{gathered}`