Math Problem Statement

4x+y+z=

−10

5, x, minus, 3, y, minus, z, equals, minus, 7

5x−3yz=

−7

6, x, plus, y, minus, z, equals, 8

6x+yz=

8

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Elimination Method

Formulas

Equation 1: 4x + y + z = -10
Equation 2: 5x - 3y - z = -7
Equation 3: 6x + y - z = 8
Addition of Equations: (4x + y + z) + (6x + y - z) = -10 + 8
Simplified Equations: 10x + 2y = -2, 11x - 2y = 1

Theorems

Elimination Method: Used to eliminate variables and reduce the system to two equations
Substitution Method: Solving one equation to substitute into another

Suitable Grade Level

Grades 9-12