Math Problem Statement

Solve for variables

Solve for variables in the system of equations: x - 5z = y, 2x = 3y + z - 6, 4y - 2z = 7 - 7x.

Solution

The solution to the system of equations is:

x=1766,y=8744,z=59132x = \frac{-17}{66}, \quad y = \frac{87}{44}, \quad z = \frac{-59}{132}

Would you like more details on how these results were derived or explanations of any specific steps?

Here are 5 related questions you could explore:

  1. How can we interpret these fractions in decimal form?
  2. How would the system change if one equation was altered, for example, 4y2z=87x4y - 2z = 8 - 7x?
  3. Can this system be solved using a different method, like substitution or elimination?
  4. What happens if you graph these equations in 3D space?
  5. Can you verify this solution by substituting the values back into the original equations?

Tip: When solving systems of linear equations, always check for consistency (whether the system has one solution, no solution, or infinitely many solutions).

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations

Formulas

Solving systems of equations using substitution and elimination methods

Theorems

Consistent and independent system theorem
Substitution theorem

Suitable Grade Level

Grades 10-12