Solving Systems of Linear Equations: 2x - 6y - 4z = 16, 4x + 6y + 5z = -27, -8x + 6y

Math Problem Statement

Solve the system of equations: 2x - 6y - 4z = 16, 4x + 6y + 5z = -27, -8x + 6y - z = -9

You have provided a system of three linear equations:

1) & \quad 2x - 6y - 4z = 16 \\ 2) & \quad 4x + 6y + 5z = -27 \\ 3) & \quad -8x + 6y - z = -9 \end{aligned}$$ I will solve this system of equations using the substitution or elimination method. Let's proceed!The solution to the system of equations is: $$x = -2, \quad y = -4, \quad z = 1$$ Would you like more details on the solving process or have any further questions? Here are some related questions for further exploration: 1. What methods are used to solve systems of equations with more than three variables? 2. How does substitution differ from the elimination method in solving systems of equations? 3. Can systems of linear equations have no solution or infinitely many solutions? When does that occur? 4. How would these equations be solved graphically? 5. What applications in physics or engineering use systems of equations like this? **Tip:** When solving systems of equations, always check for consistency to ensure that the system has a unique solution.

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Linear Algebra
Systems of Equations

Elimination method
Substitution method

Unique Solution Theorem for linear systems
Linear combinations

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