Linear algebra: solving questions that has 2 systems in it

[mroldboy]

Homework Statement

solve the 2 systems

x1 + 2x2 - 2x3 =1 x1 + 2x2 - 2x3 = 9
2x1 + 5x2 +x3 = 9 2x1 + 5x2 +x3 = 9
x1 + 3x2 + 4x3 = 9 x1 + 3x2 + 4x3 = -2

the question gives this explanation

by doing elimination on a 3x5 augmented matrix and the performing two back substitutions.

Homework Equations

I don't think I understand what this question is asking, if someone could explain what it means with its explanation it would help a lot.

This is my first week taking linear algebra as well.

The Attempt at a Solution

I thought it meant to put the two systems together, but since the 2nd row of equations are the same there would only be 5, not 6 I would use so it would be 3x5.

1 2 -2 1
2 5 1 9
1 3 4 9
1 2 -2 9
1 3 4 -2

but then that would make 2 rows
0 0 0 x
and then wouldn't it be inconsistent. But the book has answers to the question so its not that. What is this question even asking me to do? Sorry if didn't put the matrix in the right form for on here.

 

[vela]

The only difference between the two systems is the constants on the righthand side of the equations. Because the coefficient matrix is identical for both systems, you'd find you would apply exactly the same row operations to find each solution, so it makes sense just to reduce both systems at the same time using the matrix

$$\left(\begin{array}{ccc|cc} 1 & 2 & -2 & 1 & 9 \\ 2 & 5 & 1 & 9 & 9 \\ 1 & 3 & 4 & 9 & -2 \end{array}\right)$$

The fourth column consists of the constants from the first system, and the fifth column consists of the constants from the second system.