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Diketahui sistem persamaan linear

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 2 y end cell equals cell 3 straight m end cell row cell 2 x plus y end cell equals cell 3 straight n end cell end table

Jika x plus y equals 3 straight b, maka nilai b equals ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

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Pembahasan

Gunakan metode eliminasi pada kedua persamaan linear seperti berikut:

table attributes columnalign center center center center center center left end attributes row cell 3 x plus 2 y end cell equals cell 3 straight m end cell cell open vertical bar cross times 1 close vertical bar end cell cell 3 x plus 2 y end cell equals cell 3 straight m end cell row cell 2 x plus y end cell equals cell 3 straight n end cell cell open vertical bar cross times 2 close vertical bar end cell cell 4 x plus 2 y end cell equals cell 6 straight n space space space space space space space space space minus end cell row space space space space cell negative x end cell equals cell 3 straight m minus 6 straight n end cell row space space space space x equals cell negative 3 straight m plus 6 straight n end cell end table

Kemudian lakukan metode substitusi seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 2 y end cell equals cell 3 straight m end cell row cell 3 open parentheses negative 3 straight m plus 6 straight n close parentheses plus 2 straight y end cell equals cell 3 straight m end cell row cell negative 9 straight m plus 18 straight n plus 2 straight y end cell equals cell 3 straight m end cell row cell 2 straight y end cell equals cell 3 straight m plus 9 straight m minus 18 straight n end cell row cell 2 straight y end cell equals cell 12 straight m minus 18 straight n end cell row straight y equals cell fraction numerator 12 straight m minus 18 straight n over denominator 2 end fraction end cell row straight y equals cell 6 straight m minus 9 straight n end cell end table

Jika x plus y equals 3 straight b, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals cell 3 straight b end cell row cell open parentheses negative 3 straight m plus 6 straight n close parentheses plus open parentheses 6 straight m minus 9 straight n close parentheses end cell equals cell 3 straight b end cell row cell negative 3 straight m plus 6 straight m plus 6 straight n minus 9 straight n end cell equals cell 3 straight b end cell row cell 3 straight m minus 3 straight n end cell equals cell 3 straight b end cell row straight b equals cell fraction numerator 3 straight m minus 3 straight n over denominator 3 end fraction end cell row straight b equals cell straight m minus straight n end cell end table

Maka, nilai b double bond m bond n.

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