Question

Является ли решением системы уравнений x-y=4; 2x+y=5 пара чисел а)(3;-1); ,)(-1;3) ??? Пожалуйста помогите-срочноо срочно надо)))

Answer 1

X - y = 4
2x + y = 5

x = 4 + y
2x + y = 5

2(4 + y) + y = 5
8 + 2y + y = 5
3y = -3
y = -1

x = 4 - 1 = 3
(3; -1)

Answer 2

Solution for the System of Equations:

The given system of equations is: 1. x - y = 4 2. 2x + y = 5

To check if the given pairs of numbers (3, -1) and (-1, 3) are solutions to the system of equations, we can substitute the values of x and y from each pair into the equations and see if they satisfy both equations.

Let's start with the pair (3, -1): 1. For x = 3 and y = -1: - Substituting these values into the first equation: 3 - (-1) = 4, which simplifies to 4 = 4 (True) - Substituting these values into the second equation: 2*3 + (-1) = 5, which simplifies to 6 - 1 = 5 (True)

So, the pair (3, -1) is a solution to the given system of equations.

Now, let's check the pair (-1, 3): 1. For x = -1 and y = 3: - Substituting these values into the first equation: -1 - 3 = 4, which simplifies to -4 = 4 (False) - Substituting these values into the second equation: 2*(-1) + 3 = 5, which simplifies to -2 + 3 = 5 (True)

So, the pair (-1, 3) is not a solution to the given system of equations.

Conclusion: The pair of numbers (3, -1) is a solution to the system of equations, while the pair (-1, 3) is not a solution.