The given system of equations is
[tex]\begin{gathered} y=x+9\rightarrow(1) \\ y=-4x-6\rightarrow(2) \end{gathered}[/tex]
We will substitute y in equation (2) by equation (1)
[tex]x+9=-4x-6[/tex]
Now, add 4x to both sides
[tex]\begin{gathered} x+4x+9=-4x+4x-6 \\ 5x+9=-6 \end{gathered}[/tex]
Subtract 9 from both sides
[tex]\begin{gathered} 5x+9-9=-6-9 \\ 5x=-15 \end{gathered}[/tex]
Divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{-15}{5} \\ x=-3 \end{gathered}[/tex]
Substitute x by -3 in equation (1) to find y
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]
The solution of the system is (-3, 6)
