Question

Решить системы уравнений методом подстановки (фото) ​

Answer 1

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)