# How do you solve the system of equations: \begin{array}{ l }{ 3x + 2y + 4z = 11} \\ { 2x - y + 3z = 4} \\ { 5x - 3y + 5z = - 1} \end{array}?

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Enter your answer as an ordered triple.

Enter your answer as an ordered triple.

##### 1 Answer

Verify that the determinant is not zero; if so, then write an augmented matrix and perform elementary row operations, until you obtain an identity matrix on the left.

#### Explanation:

Verify that the Determinant is not zero:

The system has a unique solution.

Write the Augmented Matrix

Perform Elementary Row Operations until you obtain an Identity Matrix on the left:

We have an identity matrix on the left, therefore, we can read the solution set on the right:

Check:

This checks

The ordered triple is