Question

X+y=15 y-x=-1 решите систему​

Answer 1

$x + y = 15 \\ y - x = - 1$

Применим способ алгебраического сложения, получим

$2y = 14$

Решим уравнение с одной переменной, получим

$y = 7$

Подставим значение у в первое уравнение системы, получим

$x + 7 = 15 \\ x = 8$

Ответ: (8;7)

Answer 2

To solve the system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method:

Given the system of equations:

1. x + y = 15
2. y - x = -1

Step 1: Add the two equations together to eliminate x: (1) + (2): (x + y) + (y - x) = 15 + (-1)

Simplifying the left side: x + y + y - x = 15 - 1

Step 2: Combine like terms: 2y = 14

Step 3: Solve for y: y = 14 / 2 y = 7

Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use equation (1): x + y = 15 x + 7 = 15

Step 5: Solve for x: x = 15 - 7 x = 8

So, the solution to the system of equations is x = 8 and y = 7.