Question

2x +xy+2y=11 2x-xy+2y=5 (x*x+y*y)

Answer 1

Ответ:

23у=7х

Пошаговое объяснение:

3х+3у=21х+у=25х+25у

3у-1у=21х-3х=25х+25у

2у-25у=18х-25х

-23у=-7х

23у=7х

Answer 2

To find the value of $x^2 + y^2$, we first need to solve the given system of equations:

1. $2x + xy + 2y = 11$
2. $2x - xy + 2y = 5$

Let's proceed with solving the system:

Step 1: Subtract Equation 2 from Equation 1 to eliminate the $xy$ term: $(2x + xy + 2y) - (2x - xy + 2y) = 11 - 5$

Simplifying: $2x + xy + 2y - 2x + xy - 2y = 6$ $2xy = 6$ $xy = 3$

Step 2: Substitute the value of $xy$ into either of the original equations. Let's use Equation 1: $2x + 3 + 2y = 11$

Step 3: Rearrange and simplify the equation: $2x + 2y = 11 - 3$ $2x + 2y = 8$ $x + y = 4$

Step 4: Now, we need to find the value of $x^2 + y^2$. To do this, we square Equation 3 and then subtract $2xy$ (which we found earlier) from it: $(x + y)^2 = 4^2$ $x^2 + 2xy + y^2 = 16$ $x^2 + y^2 = 16 - 2xy$ $x^2 + y^2 = 16 - 2(3)$ $x^2 + y^2 = 16 - 6$ $x^2 + y^2 = 10$

So, the value of $x^2 + y^2$ is 10.