Solution:
Given:
Let the two numbers be represented by x and y
Hence,
[tex]\begin{gathered} The\text{ sum of two numbers is 22.} \\ This\text{ means:} \\ x+y=22...................(1) \end{gathered}[/tex]Also,
[tex]\begin{gathered} One\text{ number is two less than the other.} \\ This\text{ means:} \\ x=y-2......................(2) \end{gathered}[/tex]Solving the two equations simultaneously by substituting equation (2) into equation (1);
[tex]\begin{gathered} x+y=22 \\ (y-2)+y=22 \\ y+y-2=22 \\ 2y=22+2 \\ 2y=24 \\ Dividing\text{ both sides by y;} \\ y=\frac{24}{2} \\ y=12 \end{gathered}[/tex]To get x, substitute the value of y into equation (2).
Hence,
[tex]\begin{gathered} x=y-2 \\ x=12-2 \\ x=10 \end{gathered}[/tex]Therefore, the two numbers are {10, 12}
