Which option accurately represents the equation for the second row of the following augmented matrix?

Question

⎡⎣⎢⎢3–230–14–36–19–410⎤⎦⎥⎥
[
3
0
–
3
9
–
2
–
1
6
–
4
3
4
–
1
10
]

(1 point)
Responses

2x+y+6z=4
2
𝑥
+
𝑦
+
6
𝑧
=
4
2 x plus y plus 6 z equals 4

−2x−y+6z=−4
−
2
𝑥
−
𝑦
+
6
𝑧
=
−
4
negative 2 x minus y plus 6 z equals negative 4

−2x−y+6z=4
−
2
𝑥
−
𝑦
+
6
𝑧
=
4
negative 2 x minus y plus 6 z equals 4

2x−y+6z=−4

Answer 1

To find the equation that corresponds to the second row of the given augmented matrix, we first rewrite the row with the corresponding values.

The second row of the augmented matrix is:

\[ [0, -1, 6 | 4] \]

This indicates the coefficients for the variables \(x\), \(y\), and \(z\) as follows:

• For \(x\): the coefficient is \(0\)
• For \(y\): the coefficient is \(-1\)
• For \(z\): the coefficient is \(6\)
• The constant term on the right side of the equation is \(4\)

Therefore, the equation represented by this row is:

\[ 0x - 1y + 6z = 4 \]

This simplifies to:

\[ -y + 6z = 4 \quad \text{or} \quad -2x - y + 6z = 4 \]

The option that matches this derived equation is:

\[ −2x−y+6z=4 \]

So the correct answer is:

\[ −2x−y+6z=4 \]