Với giá trị nào của m hệ phương trình sau vô nghiệm:
(I){x+my=1mx3my=2m+3

Cách 1:D=|1mm3m|=m23m,Dx=|1m2m+33m|=2m26m

Dy=|11m2m+3|=m+3

Hệ (I) vô nghiệm khi D=0,Dx=0,Dy0.
Điều này xảy ra khi {m2+3m=0m+30m=0

Cách 2: ta cũng có thể dùng phương pháp thế giải như sau:
(I){x=1mym(1my)3my=2m+3{x=1my(m2+3m)y=m+3

Hệ (I) vô nghiệm nếu (m2+3m)y=m+3 vô nghiệm. Đều này xảy ra khi m2+3m=0m+30, tức là khi m=0

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