suppose that

number of 2 point shots is N2

number of 3 points shots is N3

thus

\(\displaystyle{N}{2}+{N}{3}={27}----------{\left({g}{i}{v}{e}{n}\right)}\)

so

\(\displaystyle{N}{2}={27}-{N}{3}-----------{\left({1}\right)}\)

scored point of 2 point shots = 2 N2

scored point of 3 point shots = 3 N3

thus

\(\displaystyle{2}{N}{2}+{3}{N}{3}={60}--------{\left({2}\right)}{\left({g}{i}{v}{e}{n}\right)}\)

compensate by N2 = 27 - N3 in ( 2 )

\(\displaystyle{2}{\left({27}-{N}{3}\right)}+{3}{N}{3}={60}\)

\(\displaystyle{54}-{2}{N}{3}+{3}{N}{3}={60}\)

\(\displaystyle{54}+{N}{3}={60}{\left({a}{d}{d}-{54}\ to\ both\ {s}{i}{d}{e}{s}\right)}\)

\(\displaystyle{N}{3}={60}-{54}={6}\)

compensate in ( 1 ) by \(N3 = 6\)

\(\displaystyle{N}{2}+{6}={27}{\left({a}{d}{d}-{6}\ to\ both\ {s}{i}{d}{e}{s}\right)}\)

\(\displaystyle{N}{2}={27}-{6}={21}\)

thus

\(\displaystyle{N}{2}={21}{\quad\text{and}\quad}{N}{3}={6}\)

answer :

number of two - point shots = 21 shots.

number of three - point shots = 6 shots.