Вправи: 1100

1100. Розв’яжи систему.

x + 13y + 13z = 14;

y + 14x + 14z = 8;

z + 15x + 15y = 8;

3x + y + z = 42;

4y + x + z = 32;

5z + x + y = 40;

z = 42 – (3x + y);

z = 32 – (x + 4y);

5z + x + y 40;

42 – 3x – y = 32 – x – 4y;

5(42 – 3x – y) + x + y;

–3x – y + x + 4y = 32 – 42;

210 – 15x – 5y + x + y = 40;

–2x + 3y = –10|• 1;

–14x – 4y = –170|: (–2);

2x – 3y = 10;

7x + 2y = 85.

2x = 3y + 10|: 2;

x = 1,5y + 5;

7 • (1,5y + 5) + 2y = 85;

10,5y + 35 + 2y = 85;

12,5y = 50;

y = 40.

x = 1,5 • 4 + 5 = 6 + 5 = 11;

z = 42 – (3 • 11 + 4) = 42 – (33 + 4) = 42 – 37 = 5.

Відповідь: (11; 4; 5).