INFORMATION:
We have the next system of equations:
[tex]\begin{cases}{x-5y=-16} \\ {9x+9y=72} \\ {4x-6z=-8}\end{cases}[/tex]
And we need to determine if (4, 4, 4) is a solution of the system.
STEP BY STEP EXPLANATION:
To know if the ordered triple is a solution of the system, we need to that (4, 4, 4) means x = 4, y = 4 and z = 4.
Then, to know if it is a solution we must replace the values on each equation to verify if the values are solutions
We have three equations:
1. x - 5y = -16
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 4-5\cdot4=-16 \\ 4-20=-16 \\ -16=-16 \\ \text{ TRUE} \end{gathered}[/tex]
2. 9x + 9y = 72
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 9\cdot4+9\cdot4=72 \\ 36+36=72 \\ 72=72 \\ \text{ TRUE} \end{gathered}[/tex]
3. 4x - 6z = -8
Replacing x = 4 and z = 4, we obtain
[tex]\begin{gathered} 4\cdot4-6\cdot4=-8 \\ 16-24=-8 \\ -8=-8 \\ \text{ TRUE} \end{gathered}[/tex]
Finally, since the three equations are true when x = 4, y = 4 and z = 4, the ordered triple is a solution
ANSWER:
Yes
