The system of equations is rewritten as a matrix, which is then converted to row echelon form, shown below:2x + 5y = 103x − y = −19137014What can be concluded from the matrix in its row echelon form?A.y + 3 = 7B.y = 4C.x = 4D.x + 3 = 7

To analyze the matrix and determine what can be concluded, we need to interpret the row echelon form provided.

We are given the system of equations:

1. \( 2x + 5y = 10 \)
2. \( 3x - y = -19 \)

The matrix corresponding to this system is:

\[
\begin{pmatrix}
2 & 5 & | & 10 \\
3 & -1 & | & -19
\end{pmatrix}
\]

In its row echelon form, the matrix is:

\[
\begin{pmatrix}
1 & 0 & | & 4 \\
0 & 1 & | & 4
\end{pmatrix}
\]

This form means that the equations have been simplified to:

1. \( x = 4 \)
2. \( y = 4 \)

Thus, the correct conclusion is:

**C. \( x = 4 \)**

Let me know if you'd like further details or clarifications!

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Here are 5 related questions:
1. How is a system of equations converted into a matrix?
2. What are the steps to reduce a matrix to row echelon form?
3. How do you interpret the row echelon form of a matrix in solving systems?
4. What are the properties of row echelon form?
5. How can we solve a system of equations with more than two variables using matrices?

**Tip:** In row echelon form, each leading entry (the first nonzero number from the left in a row) must be 1, and all entries below it must be 0.

The system of equations is rewritten as a matrix, which is then converted to row echelon form, shown below:
2x + 5y = 10
3x − y = −19
What can be concluded from the matrix in its row echelon form?
A. y + 3 = 7
B. y = 4
C. x = 4
D. x + 3 = 7

Explore how to solve a system of linear equations by converting it into a matrix and applying Gaussian elimination to obtain row echelon form. This example simplifies the equations to find x = 4 and y = 4. Suitable for Grades 9-12 students learning linear algebra.

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