Question

Решите систему

Answer 1

когда пишете в техе, приятней все выглядит, если перед синусом- косинуос ставить обратный слеш: \sin X или \cos Y :)

 

Посмотрим на второе уравнение. 

$\sin^2Y\leqslant1$

$-\cos X\leqslant1$

Тогда $\sin^2Y=1$, $\cos X=-1$.

Подставив в первое уравнение, убеждаемся, что $\cos X=\sin Y=-1$. Решаем уравнения:

$X=(2n+1)\pi,\ n\in\mathbb Z$

$Y=-\frac\pi2+2\pi k=(4k-1)\frac\pi2,\ k\in\mathbb Z$

Answer 2

Solving the System of Equations

To solve the given system of equations, we will use the information provided in the search results snippets. Let's analyze each snippet to find the solution.

Snippet from Source ``` 2x - y = 7 x^2 - xy = 12 ``` Unfortunately, this snippet does not provide enough information to solve the system.

Snippet from Source ``` 3x - y = 3 3x - 2y = 0 ``` This snippet provides a system of equations. We can solve it using the method of substitution or elimination. Let's use the elimination method:

Multiplying the first equation by 2, we get: ``` 6x - 2y = 6 3x - 2y = 0 ``` Subtracting the second equation from the first equation, we eliminate the variable y: ``` 6x - 2y - (3x - 2y) = 6 - 0 3x = 6 x = 2 ``` Substituting the value of x into the first equation, we can find the value of y: ``` 3(2) - y = 3 6 - y = 3 y = 6 - 3 y = 3 ``` Therefore, the solution to the system of equations is x = 2 and y = 3.

Snippet from Source ``` 2ab - 3a/b = 15 ab + a/b = 10 ``` This snippet provides another system of equations. However, it is not possible to solve this system without additional information.

Snippet from Source ``` 7x + 8 = 2 34x - 7 = 0 ``` This snippet provides a system of equations. Let's solve it:

Solving the first equation for x, we get: ``` 7x = 2 - 8 7x = -6 x = -6/7 ``` Substituting the value of x into the second equation, we can find the value of y: ``` 34(-6/7) - 7 = 0 -204/7 - 7 = 0 -204 - 49 = 0 -253 = 0 ``` The equation -253 = 0 is not true, which means there is no solution to this system of equations.

Snippet from Source ``` (3;-2), (7/3; -2/3) ``` This snippet provides the solution to a system of equations, but it does not correspond to the given system.

Based on the information provided in the search results snippets, we were able to solve one system of equations: x = 2 and y = 3. The other systems either did not provide enough information or did not have a solution.

If you have any further questions, feel free to ask!