`x - 3y = 5, -2x + 6y = -10` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

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Given system of equations are ,


x - 3y = 5, -2x + 6y = -10

 

so the matrix A,B are as follows,

A = 1  -3

     -2   6

and B = 5

           -10

 

so the augmented matrix is

[AB] =  1  -3    5

          -2   6   -10

step 1 . Divide the 2nd row with -2 we get

     1  -3    5         

     1   -3   5

 

Both the rows are same

step 2. subtract the the 1st row from second  row and restore the 2nd row

        1  -3    5             

        0   0    0

so , now we can say that the value of "y" is any vaule and the value of "x" is dependent on "y".

i.e x = 5+3y

And so x,y are having INFINITE number of solution sets to satisfy the system of equations given.

 

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