Question

Solve the following system of linear equations in three variables.

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

Answer 1

To solve the system of linear equations in three variables, you can use the method of elimination or substitution. The solution to the given system of equations is x = 1, y = 2, and z = 3.

Step-by-step explanation:

To solve the system of linear equations in three variables: 3x-2y+z=2, 2x+3y-z=5, x+y+z=6, we can use the method of elimination or substitution.

Method 1: Elimination

1. Add the three equations together to eliminate one variable:
2. Combine like terms to simplify:
3. Solve the resulting equation:

Method 2: Substitution

1. Solve one equation for one variable:
2. Substitute the expression from Step 1 into the other two equations:
3. Solve the resulting system of two equations in two variables:
4. Substitute the values of x and y back into one of the original equations to solve for z:

Therefore, the solution to the system of linear equations is x = 1, y = 2, and z = 3.