Question

Решить систему уравнений.

Answer 1

{ x - y + z = 2
{ x + 2y - z = 3
{ 3x - 2y + 2z = 6
Складываем 1 и 2 уравнения. 2-ое умножаем на 2 и складываем с 3-им.
{ 3x - 2y + 2z = 6
{ 2x + y = 5
{ 5x + 2y = 12
Умножаем 2-ое уравнение на -2 и складываем с 3-им.
{ 3x - 2y + 2z = 6
{ x = 2
Подставляем известное х во 2-ое уравнение
2*2 + y = 5
y = 1
Подставляем известные x и y в 1-ое уравнение
3*2 - 2*1 + 2z = 6
z = 1
Ответ: (2, 1, 1)

Answer 2

Solving the System of Equations

To solve the system of equations, we need to find the values of the variables that satisfy both equations. The system of equations you provided is:

1) x - 5xy + 4y = 0 2) 2x - y = 31

Let's solve this system step by step.

First, let's rearrange equation 2) to express y in terms of x: 2x - y = 31 y = 2x - 31

Now, substitute this expression for y in equation 1): x - 5xy + 4y = 0 x - 5x(2x - 31) + 4(2x - 31) = 0

Simplifying this equation will give us the value of x. Let's do the calculations:

x - 10x^2 + 155x + 8x - 124 = 0 -10x^2 + 163x - 124 = 0

To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -10, b = 163, and c = -124. Let's substitute these values into the formula:

x = (-163 ± √(163^2 - 4(-10)(-124))) / (2(-10))

Calculating this expression will give us the values of x. Let's do the math:

x = (-163 ± √(26569 - 4960)) / (-20) x = (-163 ± √(21609)) / (-20) x = (-163 ± 147) / (-20)

Now, we have two possible values for x. Let's calculate them:

x1 = (-163 + 147) / (-20) = -16 / (-20) = 0.8 x2 = (-163 - 147) / (-20) = -310 / (-20) = 15.5

Now that we have the values of x, we can substitute them back into equation 2) to find the corresponding values of y. Let's do that:

For x = 0.8: y = 2x - 31 y = 2(0.8) - 31 y = 1.6 - 31 y = -29.4

For x = 15.5: y = 2x - 31 y = 2(15.5) - 31 y = 31 - 31 y = 0

Therefore, the solutions to the system of equations are: (0.8, -29.4) and (15.5, 0).

I hope this helps! Let me know if you have any further questions.