Question

Решите системы уравнений: 3x-4y=-1 x+4y=5 5x-y=5 y-5x+5=0 x-y=-3 2y-2x=5 Очень нужно...Пожалуйста решите...

Answer 1

Все очень просто. Учись студент 

Answer 2

Solving the Systems of Equations

Let's solve the given systems of equations:

1. 3x - 4y = -1 x + 4y = 5

2. 5x - y = 5 y - 5x + 5 = 0

3. x - y = -3 2y - 2x = 5

Solution:

To solve the first system of equations: 1. 3x - 4y = -1 2. x + 4y = 5

We can add the two equations to eliminate the variable y: 3x - 4y + x + 4y = -1 + 5 4x = 4 x = 1

Substitute x = 1 into the second equation: 1 + 4y = 5 4y = 4 y = 1

So, the solution to the first system of equations is: x = 1 y = 1

Now, let's solve the second system of equations: 1. 5x - y = 5 2. y - 5x + 5 = 0

We can add the two equations to eliminate the variable x: 5x - y + y - 5x + 5 = 5 + 0 5 = 5

This equation simplifies to 5 = 5, which is always true. This means that the second system of equations has infinitely many solutions.

Finally, let's solve the third system of equations: 1. x - y = -3 2. 2y - 2x = 5

We can rewrite the second equation as: y - x = 5/2

Now, we can add the two equations to eliminate the variable x: x - y + y - x = -3 + 5/2 -2 = -3 + 5/2 -2 = -1/2

This equation simplifies to -2 = -1/2, which is not true. Therefore, the third system of equations has no solution.

In summary: - The first system of equations has a unique solution: x = 1 and y = 1. - The second system of equations has infinitely many solutions. - The third system of equations has no solution.

I hope this helps! If you have any further questions, feel free to ask.