Finding the solution of each equation, we have:
a)
[tex]\begin{gathered} 10x+5=3(5x+7) \\ 10x+5=15x+21 \\ 5x=-16 \\ x=-3.2 \end{gathered}[/tex]This system has one solution.
b)
[tex]\begin{gathered} 5x-10=x+20 \\ 4x=30 \\ x=7.5 \end{gathered}[/tex]This system has one solution.
c)
[tex]\begin{gathered} 2(6+x)=14+2x \\ 12+2x=14+2x \\ 12=14 \end{gathered}[/tex]This system has no solutions.
d)
[tex]\begin{gathered} 2(4+x)=8+2x \\ 8+2x=8+2x_{} \\ 8=8 \end{gathered}[/tex]This system has infinitely many solutions.
So the correct options are A and B.
