Вправи: 1092 (1-2)

1092. 1) Розв’яжіть систему рівнянь:

3x + 4y = 0, 3x = –4y, x = –43y,

2x – 7y = 29; 2x – 7y = 29; 2 ∙ (–43y) – 7y = 29│∙(–3);

x = –43y, x = –43y, x = –43y, x = –43 ∙ (–3), x = 4,

8y + 21y = –87; 29y – 87; y = –3; y = –3; y = –3.

Відповідь: (4; –3 );

2) 8x – 5y = 41, 5y = 8x – 41; y = 8x-415,

4x + 3y = –7; 4x + 3y = –7; 4x + 3 ∙ 8x-415 = –7│∙ 5;

y = 8x-415, y = 8x-415, y = 8x-415,

20x + 3(8x – 41) = –35; 20x + 24x – 123 = –35 44x = 88;

y = 8x-415, y = 8•2-415, y = –5,

x = 2; x = 2; x = 2.

Відповідь: (2; –5 );

3) 2a – 5b = 0, 2a = 5b, a = 52b,

–7a + 4b = 27; –7a + 4b = 27; –7 ∙ 52b + 4b = 27│∙2;

a = 52b, a = 52b, a = 52b, a = 52b, a = 52 ∙ (–2),

–35b + 8b = 54; –27b = 54; b = –2; b = –2; b = –2;

a = –5,

b = –2.

Відповідь: (–5 ; –2 );

4) 10m – 2n = 9, 2n = 10m – 39, n = 10m - 392,

9m + 4n = 38; 9m + 4n = 38; 9m + 4 ∙ 10m - 392 = 38;

n = 10m - 392, n = 10m - 392, n = 10m - 392,

9m + 20m – 78 = 38; 29m = 116; m = 4;

n = 10 •4-392, n = 12,

m = 4; m = 4.

Відповідь: (4;12).