Вправи: 1035(1-2)

1035. Знайдіть розв’язок системи рівнянь:

1) 4x + y = 12, y = 12 – 4x, y = 12 – 4x

7x + 2y = 20; 7x + 2y = 20; 7x + 2(12 – 4x) = 20;

y = 12 – 4x, y = 12 – 4x, y = 12 – 4 ∙ 4, y = –4,

7x + 24 – 8x = 20; –x = –4; x = 4; x = 4.

Відповідь: (4; –4);

2) x – 2y = 5, x = 2y + 5, x = 2y + 5, x = 2y + 5,

3x + 8y = 1; 3x + 8y = 1; 3(2y + 5) + 8y = 1; 6y + 15+8y = 1;

x = 2y + 5, x = 2∙ (–1) + 5, x = 3,

14y = –14; y = –1; y = –1.

Відповідь: (3; –1);

3) 4y – x = 11, x = 4y – 11, x = 4y – 11,

5x – 2y = 17; 5x – 2y = 17; 5(4y – 11) – 2y = 17;

x = 4y – 11, x = 4y – 11, x = 4 ∙ 4 – 11, x = 5,

20y – 55 – 2y = 17; 18y = 72; y = 4; y = 4.

Відповідь: (5; 4);

4) 6x – y = –1, y = 6x + 1, y = 6x + 1,

2x – 3y = –11; 2x – 3y = –11; 2x – 3(6x + 1) = –11;

y = 6x + 1, y = 6x + 1, y = 6 ∙ 05 + 1, y = 4,

2x – 18x – 3 = –11; –16x = –8; x = 0,5; x = 0,5.

Відповідь: (0,5; 4);

5) x + y = 7, x = 7 – y, x = 7 – y,

9y – 2x = –25; –2x + 9y = –25; –2(7–y) + 9y = –25;

x = 7 – y, x = 7 – y, x = 7 –(–1), x = 8,

–14 + 2y + 9y = –25; 11y = –11; y = –1; y = –1.

Відповідь: (8; –1);

6) 5x – 3y = 0, 5x = 3y, x = 0,6y,

15x + 2y = 55; 15x + 2y = 55; 15x + 2y = 55;

x = 0,6y, x = 0,6y, x = 0,6y, x = 0,6 ∙ 5, x = 3,

15 ∙ 0,6y + 2y = 55; 9y + 2y = 55; 11y = 55; y = 5; y = 5.

Відповідь: (3; 5).