Question

Найти x+y ,если x+y+2z=13 , x+2y+z=12 и 2x+y+z=11

Answer 1

Ответ:

5

Объяснение:

 сложим второе и третье уравнения : 3x +3y+2z = 23  , из

полученного уравнения вычтем первое уравнение системы :

            2x+2y = 10 ⇒  x+y = 5

Answer 2

Вот твой ответ:

x=5;

y=-6;

z=7;

Объяснение:

Answer 3

To find the values of x and y, we can solve the system of equations given:

1. x + y + 2z = 13
2. x + 2y + z = 12
3. 2x + y + z = 11

Let's solve this system of equations step by step:

Step 1: We'll use equations 2 and 3 to eliminate z.

Multiply equation 2 by 2: 2(x + 2y + z) = 2(12) => 2x + 4y + 2z = 24

Now, subtract equation 3 from the above equation: (2x + 4y + 2z) - (2x + y + z) = 24 - 11 => 3y + z = 13

Step 2: Now, let's use equation 1 to eliminate z.

Multiply equation 1 by 2: 2(x + y + 2z) = 2(13) => 2x + 2y + 4z = 26

Now, subtract equation 3 from the above equation: (2x + 2y + 4z) - (2x + y + z) = 26 - 11 => y + 3z = 15

Step 3: We now have two equations that relate y and z:

1. 3y + z = 13
2. y + 3z = 15

Step 4: Solve the above equations simultaneously to find the values of y and z.

We'll use the substitution method to solve this system:

From equation 1, we can express z in terms of y: z = 13 - 3y

Now, substitute this value of z into equation 2:

y + 3(13 - 3y) = 15

Simplify the equation:

y + 39 - 9y = 15

Combine like terms:

-8y + 39 = 15

Now, isolate y:

-8y = 15 - 39 -8y = -24

Divide by -8:

y = -24 / -8 y = 3

Step 5: Find the value of z using the value of y:

z = 13 - 3y z = 13 - 3(3) z = 13 - 9 z = 4

Step 6: Find the value of x using the value of y and z in any of the original equations. Let's use equation 1:

x + y + 2z = 13 x + 3 + 2(4) = 13 x + 3 + 8 = 13 x + 11 = 13 x = 13 - 11 x = 2

Now, we have the values of x, y, and z:

x = 2 y = 3 z = 4

Finally, let's find the sum of x and y:

x + y = 2 + 3 = 5

So, x + y = 5.