Question

Решите систему уравнений

Answer 1

I hope this helps you

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.

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

Now, substitute this value of y into Equation 2: x^2 - x(2x - 7) = 12

Simplifying the equation: x^2 - 2x^2 + 7x = 12 -x^2 + 7x = 12 x^2 - 7x + 12 = 0

Now, we can factorize the quadratic equation: (x - 3)(x - 4) = 0

Setting each factor equal to zero: x - 3 = 0 or x - 4 = 0

Solving for x: x = 3 or x = 4

Now, substitute these values of x back into Equation 1 to find the corresponding values of y.

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

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

Therefore, the solution to the system of equations is x = 3, y = -1 and x = 4, y = 1.

Note: The solution to the system of equations is not unique. There are two possible solutions: (3, -1) and (4, 1).

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