Question

X + 2y + 3 z = 6 2x-y+z=2 3x +y-3z=1​

Answer 1

Ответ: 123

Объяснение:

Answer 2

To solve the system of equations:

1. X + 2y + 3z = 6
2. 2x - y + z = 2
3. 3x + y - 3z = 1

We can use the method of elimination or substitution. Let's use the method of elimination:

Step 1: Multiply equation (2) by 2 and equation (3) by 3 to make the coefficients of x in equations (2) and (3) equal.

Equation (2) becomes: 4x - 2y + 2z = 4 Equation (3) becomes: 9x + 3y - 9z = 3

The system of equations is now:

1. X + 2y + 3z = 6
2. 4x - 2y + 2z = 4
3. 9x + 3y - 9z = 3

Step 2: Add equations (1) and (2) to eliminate y.

(X + 2y + 3z) + (4x - 2y + 2z) = 6 + 4 5x + 5z = 10 x + z = 2 (equation 4)

The system of equations now becomes:

1. X + 2y + 3z = 6
2. x + z = 2
3. 9x + 3y - 9z = 3

Step 3: Multiply equation (4) by 3 and subtract it from equation (3) to eliminate z.

(9x + 3y - 9z) - 3(x + z) = 3 - 6 9x + 3y - 9z - 3x - 3z = -3 6x + 3y - 12z = -3 2x + y - 4z = -1 (equation 5)

The system of equations now becomes:

1. X + 2y + 3z = 6
2. x + z = 2
3. 2x + y - 4z = -1

Step 4: Multiply equation (4) by 2 and subtract it from equation (5) to eliminate x.

(2x + y - 4z) - 2(x + z) = -1 - 4 2x + y - 4z - 2x - 2z = -5 y - 6z = -5 (equation 6)

The system of equations now becomes:

1. X + 2y + 3z = 6
2. x + z = 2
3. y - 6z = -5

Step 5: Solve equations (4), (6), and (1) simultaneously.

From equation (4), we have: x = 2 - z

Substituting x = 2 - z into equations (6) and (1):

y - 6z = -5 (equation 6) 2(2 - z) + 2y + 3z = 6 (equation 1)

Expanding equation (1):

4 - 2z + 2y + 3z = 6 2y + z = 2 (equation 7)

Now we have a system of two equations:

y - 6z = -5 (equation 6) 2y + z = 2 (equation 7)

Solving equations (