Answer
$(-1,3,5)$
Work Step by Step
Multiplying the first equation by $
3
$ and using the second equation, then
\begin{cases}
3x-9y+6z=0
\\
9y-z=22
.\end{cases}
Adding the two equations and using the third equation, then
\begin{cases}
3x+5z=22
\\
5x+3z=10
.\end{cases}
Multiplying the first equation above by $5$ and the second equation above by $3,$ then
\begin{cases}
15x+25z=110
\\
15x+9z=30
.\end{cases}
Subtracting the two equations above results to
\begin{array}{l}\require{cancel}
16z=80
\\
z=5
.\end{array}
Substituting $z=5$ in the second equation, $9y-z=22,$ results to
\begin{array}{l}\require{cancel}
9y-5=22
\\
9y=22+5
\\
9y=27
\\
y=\dfrac{27}{9}
\\
y=3
.\end{array}
Substituting $z=5$ in the third equation, $5x+3z=10,$ results to
\begin{array}{l}\require{cancel}
5x+3(5)=10
\\
5x+15=10
\\
5x=10-15
\\
5x=-5
\\
x=-\dfrac{5}{5}
\\
x=-1
.\end{array}
Hence, the solution is the point $
(-1,3,5)
.$
