Вправи: 1038(1-2)

1038. Знайдіть розв’язок системи рівнянь:

1) 6 – 5(x – y) = 7x + 4y, –5x + 5y – 7x – 4y = –6,

3(x + 1) – (6x + 8y) = 69 + 3y; 3x + 3 – 6x – 8y – 3y = 69;

–12x + y = –6, y = 12x – 6,

–3x –11y = 69 – 3; –3x – 11(12x – 6) = 66;

y = 12x – 6, y = 12x – 6, y = 12 ∙ 0 – 6, y = –6,

–3x – 132x + 66 = 66; 135x = 0; x = 0; x = 0.

Відповідь: (0; – 6);

2) x2 – y3 = 2│∙6, 3x – 2y = 12, 3x – 2(5x – 34) = 12,

5x – y = 34; y = 5x – 34; y = 5x – 34;

3x – 10x + 68 = 12, –7x = –56, x = 8, x = 8,

y = 5x – 34; y = 5x – 34; y = 5 ∙ 8 – 34; y = 6.

Відповідь: (8; 6);

3) 6y – 5x = 1, 6y – 5x = 1,

x-12 + 3y-x4 = –434│∙4; 2(x – 1) + 3y – x = –19;

6y – 5x = 1, 6y – 5x = 1, 6y – 5x = 1,

2x – 2 + 3y – x = –19; x + 3y = –19 + 2; x = –3y – 17;

6y – 5(–3y – 17) = 1, 6y + 15y + 85 = 1, 21y = –84,

x = –3y – 17; x = –3y – 17; x = –3y – 17;

21y = –84, y = –4, y = –4,

x = –3y – 17; x = –3 ∙(–4) – 17; x = –5.

Відповідь: (–5; –4);

4) 1,5x - 33 + 7 - 3y8 = 3│∙24, 8(1,5x – 3) + 3(7 – 3y) = 72,

2,5x - 23 – 2y + 16 = x – 0,5│∙6; 2(2,5x – 2) – (2y + 1) = 6x – 3;

12x – 24 + 21 – 9y = 72, 12x – 9y = 75 12(–2y – 2) – 9y = 75

5x – 4 – 2y – 1 = 6x – 3; –x – 2y = 2; x = –2y – 2

–24y – 24 – 9y = 75, –33y = 99, y = –3, y = –3,

x = –2y – 2; x = –2y – 2; x = –2 ∙ (–3) – 2; x = 4.

Відповідь: (4; –3).