The given system is
[tex]\mleft\{\begin{aligned}2x+y=-9 \\ 3x+5y=4\end{aligned}\mright.[/tex]
Let's isolate y in the first equation.
[tex]\begin{gathered} 2x+y=-9 \\ y=-9-2x \end{gathered}[/tex]
Then, we replace the equation we've got in the second equation of the system.
[tex]3x+5(-9-2x)=4[/tex]
Now, we solve for x.
[tex]\begin{gathered} 3x-45-10x=4 \\ -7x=4+45 \\ -7x=49 \\ x=\frac{49}{-7} \\ x=-7 \end{gathered}[/tex]
We use this value to find y.
[tex]\begin{gathered} y=-9-2(-7) \\ y=-9+14 \\ y=5 \end{gathered}[/tex]
Therefore, the solutions are x = -7 and y = 5.
