Question

Write the augmented matrix for the following system of equations.
0, equals, 7, y, minus, 5, x, minus, 8
0=
7y−5x−8
8, y, equals, 2
8y=
2

Answer 1

To write the augmented matrix for the given system of equations, we first need to express the equations in standard form. The equations given are:

1. \( 0 = 7y - 5x - 8 \)
2. \( 8y = 2 \)

Let's rearrange these equations into standard form \( Ax + By = C \):

1. Rearranging \( 0 = 7y - 5x - 8 \):
\[
5x - 7y + 8 = 0 \quad \Rightarrow \quad 5x - 7y = -8
\]

2. Rearranging \( 8y = 2 \):
\[
0x + 8y = 2
\]

Now, we can write the augmented matrix for the system of equations:
\[
\begin{bmatrix}
5 & -7 & | & -8 \\
0 & 8 & | & 2
\end{bmatrix}
\]

This matrix represents the system of equations:
\[
\begin{aligned}
5x - 7y &= -8 \\
0x + 8y &= 2
\end{aligned}
\]