Solve(cross multiplication method)
2/x+3/y=2
1/x-1/2y=1/3

Dear student
Taking 1x=u and 1y=v, the above system of equations becomes2u+3v-2=0u-12v-13=0By cross-multiplication method, we haveu3×-13--12×-2=-v2×-13-1×-2=12×-12-3×1u-1-1=-v-23+2=1-1-3u-2=-v43=1-4u-2=-14u=12and -v43=1-4v=13So, x=2 and y=3
Regards

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