Math Problem Statement

Write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2. [3 6 | 2] [1 4 | 9]

Solution

The augmented matrix given is:

3 & 6 & | & 2 \\ 1 & 4 & | & 9 \\ \end{bmatrix}$$ This represents a system of linear equations where the first row corresponds to the coefficients of $$x_1$$ and $$x_2$$ in the first equation, and the second row corresponds to the coefficients of $$x_1$$ and $$x_2$$ in the second equation. The system of linear equations is: $$3x_1 + 6x_2 = 2$$ $$x_1 + 4x_2 = 9$$ Would you like more details or clarification on any step? Here are 5 related questions for further practice: 1. How would you solve this system of equations using substitution? 2. How would you solve this system using the elimination method? 3. How would you convert this system into row-echelon form? 4. What would the solution be if you graphed these equations? 5. How would you represent this system of equations in matrix form? **Tip**: To solve systems of equations efficiently, try row reduction to simplify the augmented matrix and find the solution step by step!

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Systems of Linear Equations
Matrices

Formulas

General form of a linear equation: ax + by = c

Theorems

Gaussian Elimination

Suitable Grade Level

Grades 9-12