X = 1 hr lessons and y = 1/2 hr lessons
x + y = 35......y = 35 - x
40x + 25y = 1115
40x + 25(35 - x) = 1115
40x + 875 - 25x = 1115
40x - 25x = 1115 - 875
15x = 240
x = 240/15
x = 16 <=== there are 16 one-hr lessons
and 19 half-hr lessons
37.5
9/24=0.375
Move the decimal two places and you get 37.5%
Answer:
Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.
If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.
Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.
The answer would be the first one.
I find it easier to expand the equation (you still get the same answer).
= 2 * 7x + 2 * 3y + 2 * 3
= 14x + 6y + 6
Hope this helps!
