[tex]\boxed{Otvet:a=23,b=9}[/tex]

Способ подстановки:

[tex]\displaystyle \left \{ {{a+b=32} \atop {a-b=14}} \right. \Leftrightarrow \left \{ {{a=32-b} \atop {a-b=14}} \right.[/tex]

[tex]a-b=14\\(32-b)-b=14\\32-2b=14\\-2b=14-32\\-2b=-18|:-2\\b=9[/tex]

[tex]a+b=32\\a+9=32\\a=32-9\\a=23[/tex]

Способ сложения:

[tex]\displaystyle \left \{ {{a+b=32} \atop {a-b=14}} \right.[/tex]

[tex](a+b)+(a-b)=32+14\\a+b+a-b=46\\(a+a)+(b-b)=46\\2a=46|:2\\a=23[/tex]

[tex]a+b=32\\23+b=32\\b=32-23\\b=9[/tex]