Question

using Cramers rule , what is the value of x in the system of linear equations below? -1/2x+3y=-4 -x-y=-1

Answer 1

Cramer's rule tells you that the value of x in the system of equations

$ax+by=c\\dx+ey=f$

is given by

$x=\dfrac{ce-fb}{ae-bd}$

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

$x=\dfrac{(-4)\cdot (-1)-(-1)\cdot 3}{\frac{-1}{2}\cdot (-1)-(-1)\cdot 3}=\dfrac{7}{\left(\frac{7}{2}\right)}\\\\x=2$