By equation 1 and 3 y+2z=8 y=8−2z And x=−2+z Now putting in equation 2 α(z−2)+β(−2z+8)+7z=3 ⇒(α−2β+7)z=2α−8β+3 So equations have unique solution if α−2β+7≠0 And equations have no solution if α−2β+7=0 and 2α−8β+3≠0 And equations have infinite solution if α−2β+7=0 and 2α−8β+3=0