Question

2x^2-y^2=34 2x^2+y^2=66 Метод сложения.

Answer 1

Вот и все, готово, тадаа

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination), we need to eliminate one of the variables by adding the two equations together. The goal is to create a new equation with only one variable, which we can then solve for its value. Let's proceed step by step:

Given system of equations:

1. 2x^2 - y^2 = 34
2. 2x^2 + y^2 = 66

Step 1: Add the two equations to eliminate y^2: (2x^2 - y^2) + (2x^2 + y^2) = 34 + 66

Simplifying the equation: 4x^2 = 100

Step 2: Divide both sides by 4 to isolate x^2: x^2 = 100 / 4 x^2 = 25

Step 3: Take the square root of both sides to find x: x = ±√25 x = ±5

Now that we have the values of x, we can find the corresponding values of y by substituting x back into one of the original equations. Let's use equation (1):

2x^2 - y^2 = 34 2(5)^2 - y^2 = 34 2 * 25 - y^2 = 34 50 - y^2 = 34

Subtract 50 from both sides: -y^2 = 34 - 50 -y^2 = -16

Step 4: Multiply both sides by -1 to solve for y^2: y^2 = 16

Step 5: Take the square root of both sides to find y: y = ±√16 y = ±4

So the solutions to the system of equations are:

1. x = 5, y = 4
2. x = 5, y = -4
3. x = -5, y = 4
4. x = -5, y = -4

Therefore, there are four solutions to the system of equations using the method of addition.