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

User Rhamel
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1 Answer

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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=(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=((-4)\cdot (-1)-(-1)\cdot 3)/((-1)/(2)\cdot (-1)-(-1)\cdot 3)=(7)/(\left((7)/(2)\right))\\\\x=2

User Gene Olson
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