Question

Select the correct choice below and fill in the blank

Answer 1

For this problem we were given the following system:

`\begin{cases}5x+6y=1 \\ 10x+12y=2\end{cases}`

We need to determine how many solutions it has, and if possible find the solutions. The first step is to determine the Matrix that represents this system:

`D=\begin{bmatrix}{5} & {6} \\ {10} & {12}\end{bmatrix}`

Now we need to calculate the determinant for this Matrix:

`|D|=5\cdot12-10\cdot6=60-60=0`

Since the determinant of the system is equal to 0, then it has no solutions. The correct answer is C.