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3x + 4y – 5z = -27 2x + 3y – z = -3 6x – y + 4z = 3 ïðèìåð
ðåøåíèÿ ñèñòåìû
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Íà ïîäñòóïàõ ê îêîí÷àíèþ 12 êëàññà
Äëÿ ñàìîïîäãîòîâêè ïî ìàòåìàòèêå þíîãî
ìàòåìàòèêà
Äàíà ñèñòåìà
3-õ óðàâíåíèé ñ 3-ìÿ íåèçâåñòíûìè.
Íàéòè y.
3x + 4y – 5z = -27 (1)
2x + 3y – z = -3 (2)
6x – y + 4z = 3 (3)
Âûðàçèì z èç 2-ãî
z = 2x + 3y + 3 (4)
Ïîäñòàâèì â
1-å.
3x + 4y – 5(2x + 3y + 3) = -27 (5)
3x + 4y – 10x – 15y – 15 = - 27 (6)
-7x – 11y = -12 (7)
Ïîäñòàâèì â 3-å.
6x – y + 4(2x + 3y + 3) = 3 (8)
6x – y + 8x + 12y + 12 = 3 (9)
14x + 11y = -9 (10)
Óìíîæèì 7-å
íà 2
-14x – 22y = -24 (11)
... è ñëîæèì
ñ 10-ì
-11y
= -33 (12)
Y = 3