SOLUTION: The following matrix is obtained from a system of equations {{{(matrix(3,4, 1, 0, 6, 5, 0, 1, -4, 3,0, 0, 2, -6)) }}} The solution to the system is ___________.

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: The following matrix is obtained from a system of equations {{{(matrix(3,4, 1, 0, 6, 5, 0, 1, -4, 3,0, 0, 2, -6)) }}} The solution to the system is ___________.      Log On


   

Question 92959This question is from textbook
: The following matrix is obtained from a system of equations
%28matrix%283%2C4%2C+1%2C+0%2C+6%2C+5%2C+0%2C+1%2C+-4%2C+3%2C0%2C+0%2C++2%2C+-6%29%29+
The solution to the system is ___________. This question is from textbook

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The following matrix is obtained from a system of equations
%28matrix%283%2C4%2C+1%2C+0%2C+6%2C+5%2C+0%2C+1%2C+-4%2C+3%2C0%2C+0%2C++2%2C+-6%29%29+
The solution to the system is ___________.

This matrix is an abbreviation for

1x + 0x + 6z =  5
0x + 1y - 4z =  3
0x + 0y + 2z = -6

or, after erasing the 0 terms and the 
1 coefficients:

 x      + 6z =  5
      y - 4z =  3
          2z = -6

Solve the bottom equation for z

          2z = -6
           z = -3

Substitute that in the middle equation:

      y - 4z =  3
   y - 4(-3) =  3
      y + 12 =  3
           y = -9

Substitute z = -3 in the top equation:

 x      + 6z =  5
      x + 6z = 5
   x + 6(-3) = 5
      x - 18 = 5
           x = 23

So the solution is

(x, y, z) = (23, -9, -3)

Edwin