Let:
x = The smaller number
y = The larger number
[tex]y=3x+5_{\text{ }}(1)[/tex][tex]x+y+1=26_{\text{ }}(2)[/tex]Replace (1) into (2):
[tex]x+3x+5+1=26[/tex]Add like terms:
[tex]4x+6=26[/tex]Solve for x:
[tex]\begin{gathered} 4x=26-6 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Replace x into (1):
[tex]\begin{gathered} y=3(5)+5 \\ y=20 \end{gathered}[/tex]Answer:
The smaller number is 5
The larger number is 20
