Question 1114252
.
<pre>
1.  When solving system by the Cramer's method (=Cramer's rule), 

    the denominator in the formula is the determinant of the matrix of the system.


    So, from the referred picture, the matrix of the system is  {{{(matrix(2,2, 3,5, 5,7))}}}.


    When solving system by the Cramer's method (=Cramer's rule),

    the numerator in the formula for x is is the determinant of the matrix,

    whose first vertical column is the vector of the right hand side.


    Therefore, the system of equations is THIS:


        3x + 5y = 33,

        5x + 7y = 51.



2.  The determinant of the major matrix is 3*7 - 5*5 = 21-25 = -4.


    It is the denominator in formulas for x and y, according to the Cramer's rule.


    The determinant in the numerator for the formula for y  is

         det {{{(matrix(2,2, 3,33, 5,51))}}} = 3*51-5*33 = -12.



3.  The determinant in the numerator for the formula for x  is

         det {{{(matrix(2,2, 33,5, 51,7))}}} = 33*7-5*51 = -24.


    Therefore, the solution to the system is x = {{{(-24)/(-4)}}} = 6,  y = {{{(-12)/(-4)}}} = 3.


     <U>Check</U>:  1-st eq.: 3*6 + 5*3 = 33    ! Correct !

             2-nd eq.: 5*6 + 7*3 = 51    ! Correct !



4.  The values of x and y (= the solution to the system)  are x= 6,  y= 3.
</pre>

Solved.


I answered all the questions.


If you want to learn everything &nbsp;about the &nbsp;Cramer's &nbsp;rule &nbsp;related to &nbsp;2x2-systems of equations,

read 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.


You have rare opportunity to learn this theory and to look into examples from the best source. &nbsp;Do not miss it !


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
&nbsp;&nbsp;&nbsp;&nbsp; "<U>2x2-Matrices, determinants, Cramer's rule for systems in two unknowns</U>" 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.