Cramer's rule tells you that the value of x in the system of equations
[tex]ax+by=c\\dx+ey=f[/tex]
is given by
[tex]x=\dfrac{ce-fb}{ae-bd}[/tex]
In matrix terms, this is the determinant of the coefficient matrix with the right-side constants replacing the x-coefficients divided by the determinant of the matrix of coefficients. The value of y can be found by doing similar math with the numerator being the determinant of the coefficient matrix with the right-side constants replacing the y-coefficients. For systems of higher dimension, the column of right-side coefficients replaces each column of variable coefficients in turn.
For your equations, this evaluates to
[tex]x=\dfrac{(-4)\cdot (-1)-(-1)\cdot 3}{\frac{-1}{2}\cdot (-1)-(-1)\cdot 3}=\dfrac{7}{\left(\frac{7}{2}\right)}\\\\x=2[/tex]
