SOLUTION
Let the two intgers be x and y.
Their sum is 41
[tex]x+y=41[/tex]Their difference is 7, so
[tex]x-y=7[/tex]Making x the subject in equation 1, we have
[tex]\begin{gathered} x+y=41 \\ y=41-x \end{gathered}[/tex]Substitute y for 41 - x into equation 2, we have
[tex]\begin{gathered} x-y=7 \\ x-(41-x)=7 \\ x-41+x=7 \\ collecting\text{ like terms} \\ x+x=41+7 \\ 2x=48 \\ x=\frac{48}{2} \\ x=24 \end{gathered}[/tex]From y = 41 - x, we have
[tex]\begin{gathered} y=41-x \\ y=41-24 \\ y=17 \end{gathered}[/tex]Hence the smaller number is 17
