Given the ordered triple:
[tex](-8,-5,6)[/tex]
If we are to check if it satisfies the set of equations given:
[tex]\begin{gathered} -3y-2z=3 \\ -x+y=3 \\ 3x-3y+2z=3 \end{gathered}[/tex]
We will simply substitute the values of
[tex]\begin{gathered} x=-8,\text{ y=-5, and z=6} \\ \text{Into the left-hand sides of the equation given and then compare with the right-hand side} \end{gathered}[/tex]
For the first equation
[tex]\begin{gathered} -3(-5)-2(6)=15-12=3 \\ \text{The left-hand side equals the right-hand side } \end{gathered}[/tex]
For the second equation
[tex]\begin{gathered} -(-8)+(-5)=3 \\ \text{The left-hand side equals the right-hand side } \end{gathered}[/tex]
For the third question
[tex]\begin{gathered} 3(-8)-3(-5)+2(6)=3 \\ \text{The left-hand side equals the right-hand side } \end{gathered}[/tex]
Since the left-hand side equals the right-hand side in the three cases, the ordered triple satisfies the systems of equation.
Thus, the correct answer is Yes
