Starting from the given system of equations:
[tex]\begin{gathered} 9x+y=16 \\ y=7x \end{gathered}[/tex]Since the variable y is already isolated in the second equation, we can use the substitution method to solve the system.
Replace y by 7x on the first equation:
[tex]\begin{gathered} 9x+y=16 \\ \Rightarrow9x+7x=16 \\ \Rightarrow16x=16 \\ \Rightarrow x=1 \end{gathered}[/tex]Then. substitute the value x=1 back into the second equation to find the value of y:
[tex]\begin{gathered} y=7x \\ \Rightarrow y=7(1) \\ \Rightarrow y=7 \end{gathered}[/tex]Therefore, the solution for this system of equations is:
[tex]\begin{gathered} x=1 \\ y=7 \end{gathered}[/tex]