Simultaneous equations by elimination $$\quad a+b=7\\\underline{+\quad a-b=2\quad}\\
\quad 2a\quad=9$$ So $a=4.5$, $b=7-4.5=2.5$ so $ab=2.5\times4.5=11.25$
Simultaneous equations by substitution Numbers with a difference of 2
$a-b=2$, so $a=b+2$
$a+b=7$, so $b+(b+2)=7\Rightarrow2b+2=7\Rightarrow2b=5$, so $b=2.5$
$a=b+2=2.5+2=4.5$ so $ab=2.5\times4.5=11.25$
Numbers which add up to 7
$a+b=7$ so $b=7-a$
$a-b=2$, so $a-(7-a)=2\Rightarrow 2a-7=2\Rightarrow 2a=9$, so $a=4.5$
Trial methods Looking at pairs of numbers with a difference of 2
1 and 3 have a difference of 2, but 1 + 3 = 4 not 7
2 and 4 have a difference of 2, but 2 + 4 = 6 not 7
3 and 5 have a difference of 2, but 3 + 5 = 8 not 7
So $a$ and $b$ must be (repectively) greater than 2 and 4 but less than 3 and 5.
2.5 and 4.5 have a difference of 2, and 2.5 + 4.5 = 7
So the numbers $a$ and $b$ are 2.5 and 4.5
2$\times$4.5 = 9, and 0.5$\times$4.5 = 2.25 (since multiplying by 0.5 is the same as dividing by 2).
So 2.5$\times$4.5 = 9 + 2.25 = 11.25
Looking at pairs of numbers which add up to 7
1 + 6 = 7 but 1 and 6 have a difference of 5, not 2
2 + 5 = 7 but 2 and 5 have a difference of 3, not 2
3 + 4 = 7 but 3 and 4 have a difference of 1, not 2
So the pair $a$ and $b$ must be between the pair 2 and 5 and the pair 3 and 4.
2.5 + 4.5 = 7 and 2.5 and 4.5 have a difference of 2
So the numbers $a$ and $b$ are 2.5 and 4.5
2$\times$4.5 = 9, and 0.5$\times$4.5 = 2.25 (since multiplying by 0.5 is the same as dividing by 2).
So 2.5$\times$4.5 = 9 + 2.25 = 11.25