Question

Решите систему уравнений

Answer 1

Решение смотри в приложении

Answer 2

Solving the System of Equations

To solve the system of equations provided, we'll start by examining each equation and then proceed with the solution.

The system of equations is as follows: 1. 2x - y = 7 2. x^2 - xy = 12

Solution

To solve the system of equations, we can use the substitution method.

First, let's solve equation (1) for y: 1. 2x - y = 7 -y = 7 - 2x y = 2x - 7

Now, substitute the value of y from equation (1) into equation (2): 2. x^2 - x(2x - 7) = 12 x^2 - 2x^2 + 7x = 12 -x^2 + 7x = 12 -x^2 + 7x - 12 = 0

Now, we have a quadratic equation in terms of x. We can solve for x using the quadratic formula: D = b^2 - 4ac = (7)^2 - 4*(-1)*(-12) = 49 - 48 = 1

x = (-b ± √D) / (2a) = ( -7 ± √1 ) / (2*(-1)) = ( -7 ± 1 ) / (-2) = ( -7 + 1 ) / (-2) or ( -7 - 1 ) / (-2) = -3 or 4

So, the solutions for x are x = -3 and x = 4.

Now, substitute the values of x back into the equation y = 2x - 7 to find the corresponding y values: - When x = -3, y = 2*(-3) - 7 = -6 - 7 = -13 - When x = 4, y = 2*4 - 7 = 8 - 7 = 1

Therefore, the solutions to the system of equations are: x = -3, y = -13 x = 4, y = 1