Question

Find the solution to the system of equations.
3x-3y-z=-7
-x+3y-z=3
x + 4z=18

Answer 1

A. x=6, y=0, z=8
B. x=3, y=0, z=2
C. x=2, y=4, z=3
D. x=2, y=3, z=4

Answer 2

You can choose to set a matrix, or make the
following substitution, using your 3rd equation.

\(\large\color{black}{ \displaystyle x + 4z=18 \quad \Longrightarrow\quad \color{#558822}{x=18-4z}}\)

And then you would get this (below), in the
remaining two (1st and 2nd) equations.

\(\large\color{black}{ \displaystyle 3\left(\color{#558822}{18-4z}\right)-3y-z=-7 }\)
\(\large\color{black}{ \displaystyle -\left(\color{#558822}{18-4z}\right)+3y-z=3 }\)

By doing this you eliminate one parameter,
and thus your equation is easier to solve.