Question

Решите систему уравнений

Answer 1

Получилось не резко, но увидеть можно

Answer 2

Solving the System of Equations

To solve the system of equations, we will use the given equations and find the values of x and y that satisfy both equations.

The system of equations is as follows:

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

To solve this system, we can use various methods such as substitution, elimination, or graphing. Let's use the substitution method.

Substitution Method

Step 1: Solve one equation for one variable in terms of the other variable.

Let's solve Equation 1 for x: 2x - y = 7 2x = y + 7 x = (y + 7)/2

Step 2: Substitute the expression for x in terms of y into the other equation.

Substituting x = (y + 7)/2 into Equation 2: (x^2) - (x * y) = 12 ((y + 7)/2)^2 - ((y + 7)/2) * y = 12

Simplifying the equation: (y^2 + 14y + 49)/4 - (y^2 + 7y)/2 = 12

Step 3: Solve the resulting equation for y.

Multiplying the equation by 4 to eliminate the denominator: (y^2 + 14y + 49) - 2(y^2 + 7y) = 48 y^2 + 14y + 49 - 2y^2 - 14y = 48 -y^2 + 49 = 48 -y^2 = -1 y^2 = 1 y = ±1

So, we have two possible values for y: y = 1 and y = -1.

Step 4: Substitute the values of y back into the expression for x to find the corresponding values of x.

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

For y = -1: x = (y + 7)/2 x = (-1 + 7)/2 x = 6/2 x = 3

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

Please let me know if you need any further assistance!