Question

Solve the following system using augmented matrix methods: x+6y=−65 8x+9y=−130 1. The augmented matrix is: ⎡⎣⎢ 1 6 ∣ -65 8 9 ∣ -130 ⎤⎦⎥ 2. Save R1 and perform the row operation 8R1−R2→R2: ⎡⎣⎢ 1 6 ∣ -65 0 39 ∣ -390 ⎤⎦⎥ 3. Save R1 and perform the row operation 1/39R2→R2: ⎡⎣⎢ 1 6 ∣ -65 0 1 ∣ -10 ⎤⎦⎥ 4. Save R2 and perform the row operation R1−6R2→R1: ⎡⎣⎢ 1 0 ∣ -5 0 1 ∣ -10 ⎤⎦⎥ 4. Solve the original system: x= y=

          Solve the following system using augmented matrix methods:
x+6y=−65
8x+9y=−130


1. The augmented matrix is:
⎡⎣⎢	
1
6
∣	
-65
8
9
∣
-130
⎤⎦⎥


2. Save R1 and perform the row operation 8R1−R2→R2:
⎡⎣⎢	
1
6
∣	
-65
0
39
∣
-390
⎤⎦⎥


3. Save R1 and perform the row operation 1/39R2→R2:
⎡⎣⎢	
1
6
∣	
-65
0
1
∣
-10
⎤⎦⎥


4. Save R2 and perform the row operation R1−6R2→R1:
⎡⎣⎢	
1
0
∣	
-5
0
1
∣
-10
⎤⎦⎥


4. Solve the original system:
x= 

y=

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Added by Mark P.

College Algebra

Jay Abramson 1st Edition

Chapter 7

Instant Answer

Solved by Expert Donna Densmore

05/07/2023

Step 1

The augmented matrix is: ⎡⎣⎢⎢⎢ 1 6 ∣∣∣∣ -65 ⎤⎦⎥⎥⎥ 8 9 -130 Show more…

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Solve the following system using augmented matrix methods: x+6y=−65 8x+9y=−130 1. The augmented matrix is: ⎡⎣⎢ 1 6 ∣ -65 8 9 ∣ -130 ⎤⎦⎥ 2. Save R1 and perform the row operation 8R1−R2→R2: ⎡⎣⎢ 1 6 ∣ -65 0 39 ∣ -390 ⎤⎦⎥ 3. Save R1 and perform the row operation 1/39R2→R2: ⎡⎣⎢ 1 6 ∣ -65 0 1 ∣ -10 ⎤⎦⎥ 4. Save R2 and perform the row operation R1−6R2→R1: ⎡⎣⎢ 1 0 ∣ -5 0 1 ∣ -10 ⎤⎦⎥ 4. Solve the original system: x= y=

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00:01 Augmented matrices.

00:01 So i'm going to first write my matrix and i'm going to use the coefficients on x are 1 and 1.

00:08 On y we have 6 and 9 and then we draw a dot here for our values negative 658 and negative 130.

00:17 So our goal is to get a 1 here and here with zeros in these two positions.

00:23 All kind of ways we can do this.

00:25 I'm having difficulty finding the following the instructions that are on your screen so i'm just going to kind of look and see what we can do.

00:34 So i'm going to this is row 1 this is row 2.

00:38 So the first thing i'm going to do is subtract the two rows.

00:42 I want to maintain this 1 here and i want a 0 here so i'm going to keep row 1.

00:48 So that means i'm going to say 1, 6 and negative 658.

00:54 They're going to stay the same.

00:55 1 minus 1 is 0.

00:57 6 minus 9 is negative 3.

01:00 And then negative 658 with the negative minus negative 130 is going to be negative 528.

01:10 So now what we can do is we can take this row and divide it by negative 3.

01:15 So let's see what that's going to be here.

01:18 So i'm going to rewrite that.

01:19 Row 1 is still the same.

01:21 1, 6, 658...

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