▁one ▁degree ▁of ▁freedom . ▁ ▁Therefore , ▁the ▁critical ▁case ▁( between ▁over det erm ined ▁and ▁under det erm ined ) ▁occurs ▁when ▁the ▁number ▁of ▁equations ▁and ▁the ▁number ▁of ▁free ▁variables ▁are ▁equal . ▁For ▁every ▁variable ▁giving ▁a ▁degree ▁of ▁freedom , ▁there ▁exists ▁a ▁corresponding ▁constraint ▁removing ▁a ▁degree ▁of ▁freedom . ▁The ▁under det erm ined ▁case , ▁by ▁contrast , ▁occurs ▁when ▁the ▁system ▁has ▁been ▁under const rained — that ▁is , ▁when ▁the ▁unknown s ▁out number ▁the ▁equations . ▁ ▁Sol utions ▁of ▁under det erm ined ▁systems ▁▁ ▁An ▁under det erm ined ▁linear ▁system ▁has ▁either ▁no ▁solution ▁or ▁infinitely ▁many ▁solutions . ▁ ▁For ▁example , ▁ ▁is ▁an ▁under det erm ined ▁system ▁without ▁any ▁solution ; ▁any ▁system ▁of ▁equations ▁having ▁no ▁solution ▁is ▁said ▁to ▁be ▁incons istent . ▁On ▁the ▁other ▁hand , ▁the ▁system ▁ ▁is ▁consistent ▁and ▁has ▁an ▁inf init ude ▁of ▁solutions , ▁such ▁as ▁( x , ▁y , ▁z ) ▁= ▁( 1 , ▁− 2 , ▁ 2 ), ▁( 2 , ▁− 3 , ▁ 2 ), ▁and ▁( 3 , ▁− 4 , ▁ 2 ). ▁All ▁of ▁these ▁solutions ▁can ▁be ▁character ized ▁by ▁first ▁subtract ing ▁the ▁first ▁equation ▁from ▁the ▁second , ▁to ▁show ▁that ▁all ▁solutions ▁obey ▁z = 2 ; ▁using ▁this ▁in ▁either ▁equation ▁shows ▁that ▁any ▁value ▁of ▁y ▁is ▁possible , ▁with ▁x = – 1 – y