Solving a System of Linear Equations with Three Variables

Math Problem Statement

Solve the system of equations: -3a - b - 3c = -8, -5a + 3b + 6c = -4, -6a - 4b + c = -20.

You provided the following system of three linear equations:

-3a - b - 3c &= -8 \\ -5a + 3b + 6c &= -4 \\ -6a - 4b + c &= -20 \end{align*}$$ I will now solve this system of equations using substitution or elimination. Let's proceed with the solution. ### System of equations: $$1) \quad -3a - b - 3c = -8$$ $$2) \quad -5a + 3b + 6c = -4$$ $$3) \quad -6a - 4b + c = -20$$ I'll solve it now.The solution to the system of equations is: $$a = 2, \quad b = 2, \quad c = 0$$ Would you like a detailed explanation of the steps or have any further questions? Here are five related questions you can explore next: 1. How can this system of equations be solved using the elimination method? 2. What happens when a system of equations has no solution? 3. How can I represent this system graphically? 4. How does substitution work in solving systems of equations? 5. What are the applications of systems of equations in real-world problems? **Tip:** When solving systems of equations, always check if the system has a unique solution, infinitely many solutions, or no solution by examining the determinant or the relationships between the equations.

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Algebra
Linear Equations
Systems of Equations

Elimination Method
Substitution Method
Matrix Method

Existence and Uniqueness Theorem for Systems of Linear Equations

Grades 9-12

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