# Thread: Solving for 2 systems at once

1. ## Solving for 2 systems at once

I dont think I understand what this question is asking, if someone could explain what it means with its explanation it would help a lot.

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.

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?

2. It's asking you to solve two systems that happen to have the same coefficient matrices, but different RHS's. So take the augmented matrix suggested, namely,

$\displaystyle \left[ \begin{array}{rrr|rr} 1 &2 &-2 &1 &9\\ 2 &5 &1 &9 &9\\ 1 &3 &4 &9 &-2 \end{array} \right],$

and perform ero's on it in order to make it upper triangular. (Usual Gaussian elimination.) What do you get?

3. thanks. weird the textbook does not show any matrices with the 2 right columns at all in the first section where the question came from.

I ended up getting it triangular and getting the right answers for each system.

4. Originally Posted by DrZ
thanks. weird the textbook does not show any matrices with the 2 right columns at all in the first section where the question came from.

I ended up getting it triangular and getting the right answers for each system.
Excellent!