Solving a System of Linear Equations: 3 Variables

Math Problem Statement

-5x + 3y + 6z = 4, -3x + y + 5z = -5, -4x + 2y + z = 13

The given image shows a system of three equations with three variables:

1) &\quad -5x + 3y + 6z = 4 \\ 2) &\quad -3x + y + 5z = -5 \\ 3) &\quad -4x + 2y + z = 13 \\ \end{aligned}$$ I'll solve this system using substitution or elimination. Let me compute the solution. The solution to the system of equations is: $$x = -2, \quad y = 4, \quad z = -3$$ Would you like more details on how this solution was derived, or do you have any other questions? Here are some related questions: 1. How can you solve systems of equations using substitution? 2. What is the method of elimination in solving systems of equations? 3. How can matrices be used to solve systems of linear equations? 4. How does the determinant of a matrix relate to solving systems of equations? 5. Can a system of equations have no solution or infinitely many solutions? **Tip:** When solving a system of equations, verifying the solution by substituting the values back into the original equations helps ensure accuracy.

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Algebra
Systems of Linear Equations
Substitution Method
Elimination Method

Linear equations in the form ax + by + cz = d
Substitution or elimination methods for solving systems of equations

Gauss Elimination
Cramer's Rule

High School (Grades 9-12)

Solve System of Linear Equations: -5x + 3y + 6z = 4, -3x + y + 5z = -5, -4x + 2y + z = 13

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