Matrices Question

Question

use the matrices to solve

 

 

6x+5y=11

 

3x-2y=-8

Answer 1

6x+5y=11

3x-2y=-8

 

The matrix is set up row and column with the coefficients and constants as:

 

6   5    11     Row 1

3  -2    -8     Row 2

 

We want this to look like 

  1  0   N₁

  0  1  N₂   where N₁ and N₂ are numbers

 

We can multiply a row by a number and add it to another row to

eliminate variables.  If we multiply row 2 by -2 and add it to row 1

we will eliminate the x variable in row 2

 

   6   5    11

  -6   4    16    (Row 2)(-2)

 

   6   5    11

   0   9    27    (Row 2)(-2) + Row 1

 

   Now to make row 2 look like   0   1   N₂   multiply row 2 by 1/9

 

   6   5    11

   0   1      3

 

We now from row 2 have  0x + 1y = 3   thus   y = 3

 

Plug that back into one of the original equations and solve for x

 

6x + 5(3) = 11

6x + 15 = 11

6x = -4

x = -4/6

x = -2/3

 

Answer  (3, -2/3)