Solve the following system of equations by using Gauss- Elimination method: 3x - y + 2z = 12 x + 2y + 8z = 11 2x - 2y - z = 2

To solve the system of equations using the **Gauss-Elimination method**, follow these steps:

### System of equations:

\[
\begin{align*}
3x - y + 2z &= 12 \\
x + 2y + 8z &= 11 \\
2x - 2y - z &= 2
\end{align*}
\]

### Step 1: Write the augmented matrix

The augmented matrix for the system of equations is:

\[
\left[
\begin{array}{ccc|c}
3 & -1 & 2 & 12 \\
1 & 2  & 8 & 11 \\
2 & -2 & -

Solve the following system of equations by using Gauss-Elimination method: 3x - y + 2z = 12, x + 2y + 8z = 11, 2x - 2y - z = 2

Learn how to solve a system of linear equations using Gaussian Elimination. This example covers the equations 3x - y + 2z = 12, x + 2y + 8z = 11, and 2x - 2y - z = 2. Suitable for high school students, this problem involves converting the equations into upper triangular form and solving by back substitution.

Math Problem Statement

Solution

System of equations:

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation