The given system is
[tex]\mleft\{\begin{aligned}y=5x-3 \\ 3x-8y=24\end{aligned}\mright.[/tex]We can multiply the first equation by 8, then we sum and solve for x.
[tex]\mleft\{\begin{aligned}8y=40x-24 \\ 3x-8y=24\end{aligned}\rightarrow3x=40x\mright.[/tex]Then we, solve for x.
[tex]\begin{gathered} 40x-3x=0 \\ 27x=0 \\ x=\frac{0}{27}=0 \end{gathered}[/tex]Now we use this value to find y.
[tex]\begin{gathered} 3x-8y=24 \\ 3(0)-8y=24 \\ -8y=24 \\ y=\frac{24}{-8}=-3 \end{gathered}[/tex]