Question

Решите систему уравнений

Answer 1

Решение смотри в приложении

Answer 2

System of Equations

To solve the system of equations, we will use the information provided in the search results snippets.

The system of equations is not clearly specified in the user's query. However, based on the available search results, I will provide solutions for two different systems of equations.

# System 1:

Equation 1: 2x - y = 7 Equation 2: x^2 - xy = 12

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 1, we can express y in terms of x: y = 2x - 7

Substituting this value of y into Equation 2, we get: x^2 - x(2x - 7) = 12 x^2 - 2x^2 + 7x = 12 -x^2 + 7x - 12 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -1, b = 7, and c = -12. Substituting these values into the quadratic formula, we get: x = (-7 ± √(7^2 - 4(-1)(-12))) / (2(-1)) x = (-7 ± √(49 - 48)) / (-2) x = (-7 ± √1) / (-2) x = (-7 ± 1) / (-2)

So, we have two possible values for x: x1 = (-7 + 1) / (-2) = -6 / -2 = 3 x2 = (-7 - 1) / (-2) = -8 / -2 = 4

Now, let's substitute these values of x back into Equation 1 to find the corresponding values of y: For x = 3: 2(3) - y = 7 6 - y = 7 -y = 7 - 6 -y = 1 y = -1

For x = 4: 2(4) - y = 7 8 - y = 7 -y = 7 - 8 -y = -1 y = 1

Therefore, the solutions to the system of equations are: (x, y) = (3, -1) and (4, 1).

# System 2:

Equation 1: 3x - y = 3 Equation 2: 3x - 2y = 0

To solve this system of equations, we can again use the substitution or elimination method. Let's use the elimination method.

Multiplying Equation 1 by 2, we get: 2(3x - y) = 2(3) 6x - 2y = 6

Now, we can subtract Equation 2 from this new equation: (6x - 2y) - (3x - 2y) = 6 - 0 6x - 2y - 3x + 2y = 6 3x = 6 x = 2

Substituting this value of x into Equation 1, we get: 3(2) - y = 3 6 - y = 3 -y = 3 - 6 -y = -3 y = 3

Therefore, the solution to the system of equations is: (x, y) = (2, 3).

Please let me know if there's anything else I can help you with!