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Question 318362: Hi, Im having great difficulty with answering these matrices questions, I am having a hard time in understanding the multiplying by rows, adding and subtracting. Here is the question.
Use augmented matrices to solve the following 2x2 systems of equations. Please show all work.
A. 3x + 4y = 11
x + 3y = 2
B. x -3y = 5
4x - 12y = 13
I know what the augmented matrices are for them both, just not able to figure out the solution.
Thanks for your help4x - 12y = 20
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the task is to get 1's diagonally and zeroes everywhere else
___ I don't have the proper notational capabilities but will describe the steps
A. 1) swap rows one and two ___ [1 3 | 2] , [3 4 | 11]
___ 2) multiply row one by -3 and add to row two ___ [1 3 | 2] , [0 -5 | 5]
___ 3) multiply row two by -1/5 ___ [1 3 | 2] , [0 1 | -1]
___ 4) multiply row two by -3 and add to row one ___ [1 0 | 5] , [0 1 | -1]
B. multiplying the 1st equation by 4 gives ___ 4x - 12y = 20
___ since this is the same as the 2nd equation, but with a different constant term, there is no solution for the system
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