To simplify the calculations, you can set the following system of equations that is equivalent to the given system. Multiply the first equation by 4, and the second by 3:
[tex]\begin{gathered} 12x+20=64, \\ 12x-27y=-30. \end{gathered}[/tex]Subtracting the second equation for the first one, you get:
[tex]\begin{gathered} 12x+20-12x+27y=64+30, \\ 47y=94, \\ y=\frac{94}{47}, \\ y=2. \end{gathered}[/tex]Substituting y=2 in the first equation and solving for x, you get:
[tex]\begin{gathered} 3x+5(2)=16, \\ 3x+10=16, \\ 3x=16-10, \\ 3x=6, \\ x=\frac{6}{3}, \\ x=2. \end{gathered}[/tex]