Question

2x1+3x2+x3=12 2x1+x2+3x3=16 3x1+2x2+x3=8

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the system of equations:

1. 2x1 + 3x2 + x3 = 12
2. 2x1 + x2 + 3x3 = 16
3. 3x1 + 2x2 + x3 = 8

We can use various methods, such as substitution, elimination, or matrix methods. I'll use the elimination method to find the solution:

Step 1: Eliminate x1 from equations 1 and 2 by subtracting equation 1 from equation 2:

(2x1 + x2 + 3x3) - (2x1 + 3x2 + x3) = 16 - 12 x2 + 2x3 = 4

Step 2: Now, eliminate x1 from equations 1 and 3 by subtracting equation 1 from equation 3:

(3x1 + 2x2 + x3) - (2x1 + 3x2 + x3) = 8 - 12 x2 - 2x3 = -4

Now, we have the following two equations:

4. x2 + 2x3 = 4
5. x2 - 2x3 = -4

Step 3: Add equations 4 and 5 together to eliminate x3:

(x2 + 2x3) + (x2 - 2x3) = 4 + (-4) 2x2 = 0

Step 4: Solve for x2:

2x2 = 0 x2 = 0/2 x2 = 0

Step 5: Substitute the value of x2 back into either equation 4 or 5 to solve for x3:

Using equation 4: x2 + 2x3 = 4 0 + 2x3 = 4 2x3 = 4 x3 = 4/2 x3 = 2

Step 6: Substitute the values of x2 and x3 back into equation 1 (or any other original equation) to find x1:

Using equation 1: 2x1 + 3x2 + x3 = 12 2x1 + 3(0) + 2 = 12 2x1 + 2 = 12 2x1 = 12 - 2 2x1 = 10 x1 = 10/2 x1 = 5

So, the solution to the system of equations is: x1 = 5 x2 = 0 x3 = 2