Вправи: 1149 (2)

1149. Розв’яжіть систему рівнянь:

1) 4x – 3y = 15, 4x = 3y + 15, x = 3y + 154,

3x – 4y = 6; 3x – 4y = 6; 3 ∙ 3y+154 – 4y = 6│∙ 4;

x = 3y + 154, x = 3y + 154, x = 3y + 154,

3 ∙(3y + 15) – 16y = 24; 9y + 45 – 16y = 24; –7y = –21;

x = 3 • 3 + 154, x = 6,

y = 3; y = 3.

Відповідь: (6; 3);

2) 2x – 3y = 2, 2x = 3y + 2, x = 3y + 22,

5x + 2y = 24; 5x + 2y = 24; 5 ∙ 3y + 22 + 2y = 24│∙2;

x = 3y + 22, x = 3y + 22, x = 3y + 22,

5 ∙ (3y + 2) + 4y = 48; 15y + 10 + 4y = 48; 19y = 38;

x = 3 • 2 + 22, x = 4,

y = 2; y = 2.

Відповідь: (4; 2);

3) 5y – 6x = 4, 6x = 5y – 4 x = 5y - 46,

7x – 4y = –1; 7x – 4y = –1; 7 ∙ 5y - 46 – 4y = –1│∙6;

x = 5y - 46, x = 5y - 46, x = 5y - 46,

7 ∙ (5y – 4) – 24y = –6; 35y – 28 – 24y = –6; 11y = 22;

x = 5 • 2 - 46, x = 1,

y = 2; y = 2.

Відповідь: (1; 2);

4) 4x + 5y = 1, 4x + 5y = 1, 4x + 5y = 1, 4x + 5(4x – 19) = 1,

8x – 2y = 38; 4x – y = 19; y = 4x – 19; y = 4x – 19;

4x + 20x – 95 = 1, 24x = 96, x = 4, x = 4,

y = 4x – 19; y = 4x – 19 y = 4 ∙ 4 – 19; y = –3.

Відповідь: (4; –3);

5) 5a – 4b = 3, 5a = 4b + 3, a = 4b + 35,

2a – 3b = 11; 2a – 3b = 11; 2 ∙ 4b + 35 – 3b = 11│∙5;

a = 4b + 35, a = 4b + 35, a = 4b + 35,

2 ∙ (4b + 3) – 15b = 55; 8b + 6 – 15b = 55; –7b = 49;

a = 4 • -7 + 35, a = –5,

b = –7; b = –7.

Відповідь: (–5 –7);

6) 8m – 2n = 11, 8m = 2n + 11, m = 2n + 118,

9m + 4n = 8; 9m + 4n = 8; 9 ∙ 2n + 118 + 4n = 8│∙ 8;

m = 2n + 118, m = 2n + 118, m = 2n + 118,

9 ∙ (2n + 11) + 32n = 64; 18n + 99 + 32n = 64; 50n = – 35;

m = 2 • -0,7 + 118, m = 1,2,

n = – 0,7; n = –0,7.

Відповідь: (1,2;–0,7).