Solve the equations 3x + 2y = 4 and x - y = 2 using Cramer's rule.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The set of linear equations 3x + 2y = 4 and x - y = 2 have to be solved using Cramer's rule.

In matrix form the system can be written as:

`[[3, 2],[1, -1]]*[[x],[y]] = [[4],[2]]`

`x = |[4,2],[2, -1]|/|[3,2],[1,-1]|`

=> `(-4 - 4)/(-3 - 2)`

=> `8/5`

`y = |[3,4],[1, 2]|/|[3,2],[1,-1]|`

=> `(6 - 4)/(-3-2)`

=> `-2/5`

The solution of the system of equations is x = 8/5 and y = -2/5

wimudu's profile pic

wimudu | Student, Undergraduate | (Level 1) eNoter

Posted on

3  2

1  -1

D= (3*-1)-(2*1)=-5  (expanding)

Dx= 4  2

        2 -1

  expanding  Dx= -8

x=Dx/D
  =8/5

Dy=3 4

      1 2

expanding Dy= 2

Y=Dy/D= -2/5

 

 

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