Math Problem Statement

Solve the system of equations: 1. x + y + z = -5 2. -2x - y + z = -1 3. x - 2y - z = 0

Solution

We are tasked with solving the system of three linear equations:

1. \quad & x + y + z = -5 \\ 2. \quad & -2x - y + z = -1 \\ 3. \quad & x - 2y - z = 0 \end{aligned}$$ Let's solve this system step by step using substitution or elimination. I'll start by reducing the system and finding the values for $$x$$, $$y$$, and $$z$$. First, I'll subtract equations from one another to eliminate one variable and solve for the remaining ones. Let's calculate. The solution to the system of equations is: $$x = -2, \quad y = 1, \quad z = -4$$ Would you like further details or explanations on the method used? Here are 5 related questions to deepen your understanding: 1. How can substitution be applied to solve a system of three equations? 2. What is the elimination method, and how does it simplify solving systems of equations? 3. How can you check the solution of a system of equations? 4. What role does matrix algebra play in solving larger systems of equations? 5. How do systems of equations apply to real-world problems, such as in physics or economics? **Tip:** Always verify your solution by substituting the values back into the original equations!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Systems of Equations
Substitution
Elimination

Formulas

System of linear equations

Theorems

Method of Substitution
Method of Elimination

Suitable Grade Level

Grades 9-12