SOLUTION
Let the smaller number be x
Let the larger number be y
Since the larger number is 31 more than 5 times the smaller number, it folllows:
[tex]y=5x+31[/tex]The sum of the two integers is 463, it follows
[tex]x+y=463[/tex]Substitute y=5x+31 into the equation
[tex]x+5x+31=463[/tex]Solve for x
[tex]\begin{gathered} 6x=463-31 \\ 6x=432 \\ x=\frac{432}{6} \\ x=72 \end{gathered}[/tex]Substitute x=72 into y=5x+31
[tex]\begin{gathered} y=5\left(72\right)+31 \\ y=360+31 \\ y=391 \end{gathered}[/tex]Therefore the two integers are 72 and 391
