Let x be the length of the longer piece and y the length of the shorter one. Then we have:
[tex]\begin{gathered} i)\text{ }x+y=24 \\ ii)\text{ }x-y=2 \end{gathered}[/tex]
Adding equation i to equation ii, we have:
[tex]\begin{gathered} x+x+y-y=24+2 \\ 2x=26 \\ x=13\text{ cm} \end{gathered}[/tex]
Applying this result in equation i, we have:
[tex]\begin{gathered} 13+y=24 \\ y=11\text{ cm} \end{gathered}[/tex]
Therefore, the length of the shorter piece is 11 cm
