[tex]\displaystyle a+b=1,(6) \\ a+b= \frac{5}{3} \\ a-b=0,(3) \\ a-b= \frac{1}{3} \\ \left \{ {{a+b= \frac{5}{3} } \atop {a-b= \frac{1}{3} }} \right. \\ 2a/= \frac{6}{3} \\ 2a=2 \\ a= \frac{2}{2} \\ a=1 \\ 1+b= \frac{5}{3} \\ 3+3b=5 \\ 3b=5-3 \\ 3b=2 \\ b= \frac{2}{3} [/tex]
[tex]\displaystyle \boxed{a=1;b= \frac{2}{3} }[/tex]
