Question

Знайдіть розв'язки рівнянь {y=x² {y=-x+2​ Смотреть ответ anjikkingg anjikkingg Ответ: x = -2, y = 4 x = 1, y = 1 Объяснение: y = y = -x + 2  = y x + y = 2 x = -2, y = 4 x = 1, y = 1

Answer 1

Solutions to the Equations

The given equations are:

1. y = x² 2. y = -x + 2

To find the solutions, we need to find the values of x and y that satisfy both equations simultaneously.

Let's solve the equations step by step:

1. y = x²

This equation represents a parabola. The graph of this equation is a U-shaped curve. The values of x and y that satisfy this equation lie on this curve.

2. y = -x + 2

This equation represents a straight line. The graph of this equation is a diagonal line with a negative slope. The values of x and y that satisfy this equation lie on this line.

To find the solutions, we need to find the points where the parabola and the line intersect. These points will satisfy both equations simultaneously.

Let's solve the equations algebraically:

1. Substitute the value of y from the second equation into the first equation:

x² = -x + 2

2. Rearrange the equation to bring all terms to one side:

x² + x - 2 = 0

3. Factorize the quadratic equation:

(x + 2)(x - 1) = 0

This equation can be satisfied when either x + 2 = 0 or x - 1 = 0.

4. Solve for x:

- When x + 2 = 0, we have x = -2. - When x - 1 = 0, we have x = 1.

5. Substitute the values of x back into the second equation to find the corresponding values of y:

- For x = -2, we have y = -(-2) + 2 = 4. - For x = 1, we have y = -(1) + 2 = 1.

Therefore, the solutions to the given equations are:

- x = -2, y = 4 - x = 1, y = 1

These are the points where the parabola and the line intersect.

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