Question

Find the complete solution of the linear system, or show that it is inconsistent. { x-y+2 z =2 { 3 x+y+5 z =8 { 2 x-y-2 z =-7

Answer 1

To find the complete solution of the given linear system or determine if it is inconsistent, you can use the method of elimination or substitution. Follow the steps outlined in the answer to solve the system of equations and obtain the values of x, y, and z.

Step-by-step explanation:

To find the complete solution of the given linear system or determine if it is inconsistent, we can use the method of elimination or substitution. Let's use the method of elimination:

1. Add the first equation to the second equation: (x - y + 2z) + (3x + y + 5z) = 2 + 8.
2. Combine like terms: 4x + 7z = 10.
3. Add the second equation to the third equation: (3x + y + 5z) + (2x - y - 2z) = 8 - 7.
4. Combine like terms: 5x + 3z = 1.
5. Solve the system of equations 4x + 7z = 10 and 5x + 3z = 1 using any method (elimination, substitution, or graphing) to find the values of x and z.
6. Once x and z are known, substitute these values back into any of the original equations to solve for y.
7. If we obtain values for x, y, and z, then it is a consistent system with a unique solution. If the system is inconsistent (no solution), then there will be a contradiction in the equations.

Thus, the step-by-step solution will yield the complete solution of the system or show that it is inconsistent.