Решить системы уравнений методом подстановки (фото)

Ответ:

1) (2; 5)

2) (4; -3)

3) (0; -6)

Объяснение:

1) $\left \{ {{y = 3x - 1} \atop {2x + y = 9}} \right.$

2x + (3x - 1) = 9

2x + 3x - 1 = 9

2x + 3x = 9 + 1

5x = 10

x = 10/5 = 2

y = 3x - 1 = 3 * 2 - 1 = 6 - 1 = 5

Ответ: (2; 5)

2) $\left \{ {{4x + 5y = 1} \atop {8x - 2y = 38}} \right$

$\left \{ {{4x + 5y = 1} \atop {4x - y = 19}} \right.$

$\left \{ {{4x + 5y = 1} \atop {y = 4x - 19}} \right.$

4x + 5(4x - 19) = 1

4x + 20x - 95 = 1

4x + 20x = 1 + 95

24x = 96

x = 96/24 = 4

y = 4x - 19 = 4 * 4 - 19 = 16 - 19 = -3

Ответ: (4; -3)

3) $\left \{ {{6 - 5(x - y) = 7x + 4y} \atop {3(x + 1) - 6x + 8y} = 69 + 3y} \right.$

6 - 5(x - y) = 7x + 4y

6 - 5x + 5y = 7x + 4y

-5x + 5y - 7x - 4y = -6

-12x + y = -6

3(x + 1) - (6x + 8y) = 69 + 3y

3x + 3 - 6x - 8y = 69 + 3y

3x - 6x - 8y - 3y = 69 - 3

-3x - 11y = 66

$\left \{ {{-12x + y = -6} \atop {-3x - 11y = 66}} \right.$

$\left \{ {{y = -6 + 12x} \atop {-3x - 11y = 66}} \right.$

-3x - 11(-6 + 12x) = 66

-3x + 66 - 132x = 66

-3x - 132x = 66 - 66

-135x = 0

x = 0

y = -6 + 12x = -6 + 12 * 0 = -6 + 0 = -6

Ответ: (0; -6)

Решить системы уравнений методом подстановки (фото) ​