Question 1156102
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<pre>

First, calculate the determinant of the coefficient matrix

    D = det {{{(matrix(2,2, 5,4, 3,6))}}} = 5*6 - 3*4 = 30 - 12 = 18.



Next, calculate the determinant Dx, replacing first column in the coefficient matrix by the right side vector

    Dx = det {{{(matrix(2,2, -14,4,  6,6))}}} = -14*6 - 4*6 = -84 - 24 = -108.



Next, calculate the determinant Dy, replacing second column in the coefficient matrix by the right side vector

    Dy = det {{{(matrix(2,2, 5,-14,  3,6))}}} = 5*6 - (-14)*3 = 30 - (-42) = 72.



Now the solution is  x = {{{Dx/D}}} = {{{-108/18}}} = -6;  y = {{{Dy/D}}} = {{{72/18}}} = 4.



<U>ANSWER</U>.  x = -6,  y = 4.
</pre>

Solved.


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On Cramer's rule for solving 2x2-system of equations, see the lesson


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of the linear system of two equations in two unknowns using determinant</A> 


and the lessons


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/What-is-a-matrix.lesson>What is a matrix?</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Determinant-of-a-2x2-matrix.lesson>Determinant of a 2x2-matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/HOW-TO-solve-system-of-linear-eqns-in-two-unknowns-using-det.lesson>HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-two-unknowns-using-Cramer%27s-rule.lesson>Solving systems of linear equations in two unknowns using the Cramer's rule</A> 


in this site.