Question

X-y+3z=-4 2x+y-2z=5 3x+3y+z=6

Answer 1

Ответ:

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Answer 2

To solve the system of equations:

1. Rearrange the equations in standard form:

   Equation 1: x - y + 3z = -4 Equation 2: 2x + y - 2z = 5 Equation 3: 3x + 3y + z = 6

2. You can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Here, we'll use the elimination method.

   Multiply Equation 1 by 2 to make the coefficients of x in Equation 1 and Equation 2 equal:

   Equation 1: 2x - 2y + 6z = -8 Equation 2: 2x + y - 2z = 5

   Subtract Equation 1 from Equation 2 to eliminate the x variable:

   (2x + y - 2z) - (2x - 2y + 6z) = 5 - (-8) y - 8z = 13 -----> Equation 4

3. Multiply Equation 1 by 3 and subtract Equation 3 from it to eliminate the x variable:

   (3x - 3y + 9z) - (3x + 3y + z) = -12 - 6 -6y + 8z = -18 -----> Equation 5

4. Now, we have two equations in terms of y and z:

   Equation 4: y - 8z = 13 Equation 5: -6y + 8z = -18

5. Add Equation 4 and Equation 5 to eliminate the z variable:

   (y - 8z) + (-6y + 8z) = 13 - 18 -5y = -5 y = 1

6. Substitute the value of y = 1 into Equation 4 to solve for z:

   1 - 8z = 13 -8z = 12 z = -1.5

7. Substitute the values of y = 1 and z = -1.5 into any of the original equations to solve for x. Let's use Equation 1:

   x - 1 + 3(-1.5) = -4 x - 1 - 4.5 = -4 x - 5.5 = -4 x = 0.5

8. The solution to the system of equations is x = 0.5, y = 1, and z = -1.5.