Question

Решите систему: x-y=4 x²+y²=20²

Answer 1

Решение задания приложено. Рисунок не нужен, если не просят графически. Это для демонстрации, что два решения.

Answer 2

To solve the system of equations, we'll use the method of substitution or elimination. Let's use the substitution method:

Step 1: Solve one equation for one variable in terms of the other variable. Step 2: Substitute that expression into the other equation. Step 3: Solve the resulting equation for one variable. Step 4: Substitute the value found back into the expression from Step 1 to find the other variable's value.

Let's begin:

Given system of equations:

1. x - y = 4
2. x² + y² = 20²

Step 1: Solve the first equation for x in terms of y. x = y + 4

Step 2: Substitute the value of x from Step 1 into the second equation. (y + 4)² + y² = 20²

Step 3: Expand and simplify the equation. y² + 8y + 16 + y² = 400 2y² + 8y - 384 = 0

Step 4: Solve the quadratic equation for y. To solve this quadratic equation, we can divide the entire equation by 2: y² + 4y - 192 = 0

Now, we can either factor the quadratic or use the quadratic formula to find the values of y. Factoring this equation, we get: (y + 16)(y - 12) = 0

Setting each factor to zero and solving for y:

1. y + 16 = 0 => y = -16
2. y - 12 = 0 => y = 12

Step 5: Find the corresponding values of x using the expression from Step 1. For y = -16: x = (-16) + 4 = -12

For y = 12: x = 12 + 4 = 16

So, the solutions to the system of equations are: x = -12, y = -16 x = 16, y = 12