Answer: The number of books bought were 9 paperbacks and 3 hardbacks
Step-by-step explanation: We shall start by assigning letters to the unknown variables, hence let the hardback be called h, while the paperback shall be called p.
If Marla bought 12 books at the garage sale, that means she bought
h + p = 12 ------(1)
Then she paid 0.5 dollars for paperback and 0.75 dollars for hardback and the total spent was 6.75 dollars for all of them, then we can express these as follows;
0.5p + 0.75h = 6.75 ------(2)
We now have a pair of simultaneous equations which are
h + p = 12 ------(1)
0.5p + 0.75h = 6.75 ------(2)
From equation (1), make h the subject of the equation,
h = 12- p
Substitute for h into equation (2)
0.5p + 0.75(12 - p) = 6.75
0.5p + 9 - 0.75p = 6.75
0.5p - 0.75p = 6.75 - 9
-0.25p = -2.25
Divide both sides of the equation by -0.25
p = 9
Now, substitute for p into equation (1)
h + p = 12
h + 9 = 12
Subtract 9 from both sides of the equation
h = 3
Therefore Marla bought 9 paperbacks and 3 hardbacks
is invertible, then we can simply choose 
because for any invertible matrix 
by definition we must have 
.
, as
