Answered

Match each system of equations to its solution represented by an augmented matrix.

1.
[tex]\[
\begin{aligned}
x + y + z &= 1,100 \\
x - 2y - z &= -500 \\
2x + 3y + 2z &= 2,600
\end{aligned}
\][/tex]

2.
[tex]\[
\begin{aligned}
x + y + z &= 2,600 \\
x + y - z &= 600 \\
2x + y + 2z &= 4,350
\end{aligned}
\][/tex]

3.
[tex]\[
\begin{aligned}
x + y + z &= 2,600 \\
x + y - z &= 600 \\
2x + y + 2z &= 3,050
\end{aligned}
\][/tex]

4.
[tex]\[
\begin{aligned}
x + y + z &= 1,900 \\
x - y - 2z &= -2,000 \\
2x + 2y + z &= 2,900
\end{aligned}
\][/tex]

5.
[tex]\[
\begin{aligned}
x + y + z &= 3,300 \\
x + y - z &= 1,500 \\
2x + 3y + 2z &= 7,700
\end{aligned}
\][/tex]

6.
[tex]\[
\begin{aligned}
x + y + z &= 1,900 \\
x - y - 2z &= -2,000 \\
2x + 2y + z &= 1,100
\end{aligned}
\][/tex]

Solution Matrices:

A.
[tex]\[
\left[\begin{array}{ccc|c}
1 & 0 & 0 & 750 \\
0 & 1 & 0 & 850 \\
0 & 0 & 1 & 1,000
\end{array}\right]
\][/tex]

B.
[tex]\[
\left[\begin{array}{ccc|c}
1 & 0 & 0 & 500 \\
0 & 1 & 0 & 400 \\
0 & 0 & 1 & 200
\end{array}\right]
\][/tex]

C.
[tex]\[
\left[\begin{array}{ccc|c}
1 & 0 & 0 & 400 \\
0 & 1 & 0 & 600 \\
0 & 0 & 1 & 900
\end{array}\right]
\][/tex]

D.
[tex]\[
\left[\begin{array}{ccc|c}
1 & 0 & 0 & 1,300 \\
0 & 1 & 0 & 1,100 \\
0 & 0 & 1 & 900
\end{array}\right]
\][/tex]

Match each system of equations with its corresponding augmented matrix by placing the correct letter (A, B, C, or D) in the squares provided:

[tex]\[
\begin{array}{ccc}
\text{System 1:} & \square \\
\text{System 2:} & \square \\
\text{System 3:} & \square \\
\text{System 4:} & \square \\
\text{System 5:} & \square \\
\text{System 6:} & \square \\
\end{array}
\][/tex]



Answer :

GinnyAnswer
Let's match each system of equations to its solution represented by an augmented matrix step-by-step.

### System of Equations 1:
[tex]\[ \begin{aligned} x + y + z & = 1100 \\ x - 2y - z & = -500 \\ 2x + 3y + 2z & = 2600 \\ \end{aligned} \][/tex]

Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1000 \end{array}\right] \][/tex]

### System of Equations 2:
[tex]\[ \begin{aligned} x + y + z & = 2600 \\ x + y - z & = 600 \\ 2x + y + 2z & = 4350 \\ \end{aligned} \][/tex]

Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]

### System of Equations 3:
[tex]\[ \begin{aligned} x + y + z & = 1900 \\ x - y - 2z & = -2000 \\ 2x + 2y + z & = 2900 \\ \end{aligned} \][/tex]

Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]

### System of Equations 4:
[tex]\[ \begin{aligned} x + y + z & = 3300 \\ x + y - z & = 1500 \\ 2x + 3y + 2z & = 7700 \\ \end{aligned} \][/tex]

Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]

### Summary

1. System of Equations 1:
[tex]\[ \begin{aligned} x + y + z & = 1100 \\ x - 2y - z & = -500 \\ 2x + 3y + 2z & = 2600 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1000 \end{array}\right] \][/tex]

2. System of Equations 2:
[tex]\[ \begin{aligned} x + y + z & = 2600 \\ x + y - z & = 600 \\ 2x + y + 2z & = 4350 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]

3. System of Equations 3:
[tex]\[ \begin{aligned} x + y + z & = 1900 \\ x - y - 2z & = -2000 \\ 2x + 2y + z & = 2900 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]

4. System of Equations 4:
[tex]\[ \begin{aligned} x + y + z & = 3300 \\ x + y - z & = 1500 \\ 2x + 3y + 2z & = 7700 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]