HELP: Supposed to solve using Matrix...

Question

In a recent game at your community college, the men’s basketball team made 45 baskets from the field; some were 2-pointers and some were 3-pointers. In total, 101 points were made from the field. The coach wanted to know how many were 2-pointers and how many were 3-pointers.

Answer 1

2x + 3y = 101

x + y = 45

 

 

2  3   [x]    101

 

1 1    [y]    45

 

 

 

A-! = 1/det A [ 1   -3]

                    [-1    2]

 

A-1 = (1 / (2 - 3)) [1  -3]

                           [ -1 2]

 

A-1 = -1 [ 1    -3 ]

              [-1    2]

 

A-1  = [ -1    3]

          [  1    -2]

 

 

A-1 [101]

      [ 45 ]

 

[-1    3]   [101]

[ 1    -2]  [45]

 

 

[ -101 + 135]

[  101 - 90 ]

 

[34]

[11]

 

x = 34

y = 11

 

34 + 11 = 45

 

34(2) + 11(3) = 68 + 33 = 101