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Select the correct choice below and fill in the blank

Select the correct choice below and fill in the blank-example-1

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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.

User Sergey Stadnik
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