If the larger number is x, and the smaller one is y, then what we have is;
[tex]\begin{gathered} x+y=8---(1)\text{ both add up to 8} \\ x-y=6---(2)\text{ both have a difference of 6} \\ \text{From equation (1), make x the subject,} \\ x=8-y \\ \text{Substitute for the value of x into equation (2)} \\ x-y=6 \\ (8-y)-y=6 \\ 8-y-y=6 \\ 8-2y=6 \\ 8-6=2y \\ 2=2y \\ \text{Divide both sides by 2} \\ y=1 \\ \text{If x+y=8, then when y=1} \\ x+1=8 \\ x=8-1 \\ x=7 \end{gathered}[/tex]Therefore, the numbers are 7 and 1
