Вправи: 1037(1)

1037. Розв’яжіть систему рівнянь:

1) 5x + 2y = 15, 5x = 15 – 2y, x = 15 - 2y5,

8x + 3y = 20; 8x + 3y = 20; 8 ∙ 15 - 2y5 + 3y = 20│∙5;

x = 15-2y5, x = 15-2y5, x = 15-2y5,

8 ∙ (15 – 2y) + 15y = 100; 120 – 16y + 15y = 100; –y = –20;

x = 15 - 2 • 205, x = –5,

y = 20; y = 20.

Відповідь: (–5; 20);

2) 7x + 4y = 5, 7x = 5 – 4y, x = 5 - 4y7,

3x + 2y = 3; 3x + 2y = 3; 3 ∙ 5 - 4y7 + 2y = 3│∙7;

x = 5 - 4y7, x = 5 - 4y7, x = 5 - 4y7,

3 ∙(5 – 4y) + 14y = 21; 15 – 12y + 14y = 21; 2y = 6;

x = 5 - 4 • 37, x = –1,

y = 3; y = 3.

Відповідь: (–1; 3);

3) 8p – 5q = –11, 8p = 5q – 11, p = 5q - 118,

5p – 4q = –6; 5p – 4q = –6 5 ∙ 5q - 118 – 4q = –6│∙8;

p = 5q-118, p = 5q-118, p = 5q- 118, p = 5 • -1 - 118,

25q – 55 – 32q = –48; –7q = 7; q = –1; q = –1;

p = –2,

q = –1.

Відповідь: (–2; –1);

4) 6u – 5v = –38, 6u = 5v – 38, u = 5v - 386,

2u + 7v = 22; 2u + 7v = 22; 2 ∙ 5v - 386 + 7v = 22│∙6;

u = 5v - 386, u = 5v - 386, u = 5v - 386,

2 ∙ (5v – 38) + 42v = 132; 10v – 76 + 42v = 132; 52v = 208;

u = 5 • 4 - 386, u = –3,

v = 4; v = 4.

Відповідь: (–3; 4).