The equations x+4y−2z=3 , 3x+y+5z=7  and 2x+3y+z=5  has

Augmented matrix is 14−2315231     375~14−20−11110−55     3−2−1 Operating R2→R2−3R1  ,R3→R3−2R1  and R3→R3−(511R2)~14−20−1111000     3−2−111⇒ ρ(A)=2  and ρ(A/B)=3 .So, the given system is inconsistent.Alternatively, it will be found that det A=0  but det A1≠0 .