Question

2x-y²=5, x+y²=16 способом подстановки.

Answer 1

-Y^2=x-16 подставляешь в первое уравнение.
Получается 2x+x-16=5
3x=21
X=7
2x-y^2=5, x=7
2*7-y^2=5
9=y^2
Y=квадратный корень из 9
Y=+\-3
Ответ: x=7; y1=3; y2=-3

Answer 2

To solve the system of equations 2x - y² = 5 and x + y² = 16 by substitution, we can isolate one variable in one equation and substitute it into the other equation. Here's the step-by-step solution:

1. Solve the second equation for x: x = 16 - y²

2. Substitute the value of x from step 1 into the first equation: 2(16 - y²) - y² = 5

3. Simplify the equation: 32 - 2y² - y² = 5 32 - 3y² = 5

4. Rearrange the equation: 3y² = 32 - 5 3y² = 27

5. Divide both sides of the equation by 3: y² = 27/3 y² = 9

6. Take the square root of both sides: y = ±√9 y = ±3

7. Substitute the values of y into the second equation to find x: For y = 3: x + (3)² = 16 x + 9 = 16 x = 16 - 9 x = 7

   For y = -3: x + (-3)² = 16 x + 9 = 16 x = 16 - 9 x = 7

8. The solutions to the system of equations are: x = 7, y = 3 x = 7, y = -3

Therefore, the system of equations has two solutions: (7, 3) and (7, -3).