1. Use back-substitution to solve the system. Express your answer as an ordered triple $(x, y, z)$. $2x + z = 5$ $3y + 2z = 6$ $5x = 20$ Solution: ___
2. Use back-substitution to solve the system. Express your answer as an ordered triple $(x, y, z)$. $2x + 3y - z = -7$ $y - 2z = -6$ $5z = 15$ Solution: ___
3. Use back-substitution to solve the system of equations. What is the value of $x$? $x+y-z=1$ $y+2z=10$ $3z=18$ $x = $ ___
4. When using back-substitution to solve the system below, which variable must be found first? $x - 2y + z = 10$ $4y - z = 7$ $3z = 9$
5. Solve the system using back-substitution: $x+y+z=10$ $2y-z=4$ $2z=5$ The solution is $(x, y, z) = ($___$, 3.25, 2.5)$.
6. Consider the system: $x + y + z = 12$ $2y + z = 8$ $z = 4$ Using back-substitution, what is the value of $y$?
7. Solve the system of equations using back-substitution: $2x - y + z = 6$ $3y - 2z = 9$ $-4z = -12$ The solution is $(x, y, z) = (4, 5, $___$)$.
8. Is the ordered triple $(2, 1, 4)$ a solution to the system of equations $x+y+z=7$, $2x-y+z=7$, and $x-y-z=-3$?
9. The ordered triple $(x, 4, 1)$ is the solution to the system with equations $x+y+z=6$ and $2x-y+3z=1$. What is the value of $x$? ___
10. The ordered triple $(3, 0, 5)$ is not a solution to the system below. Which equation does it fail to satisfy? $\begin{cases} x+y+z=8 \\ 2x-y-z=1 \\ x-y+z=7 \end{cases}$