Question 1162531
.


            Although the post is silent on what  Dy  is,  I will assume that  Dy  is the determinant of a matrix 
            from the  "Cramer's rule" / "Cramer's solution".



<U>Solution</U>


<pre>
<U>Step 1</U>.  Write the system in the canonical form


    -4x + 7y =  1

     2x + 5y = 25



<U>Step 2</U>.  Write the coefficient matrix of the system


    A = {{{(matrix(2,2,  -4,7,  2,5))}}}



<U>Step 3</U>.  In matrix A, replace the second column by the right side vector

    
     Ay = {{{(matrix(2,2, -4,1,  2,25))}}}.



<U>Step 4</U>.  Now Dy is the determinant of the matrix Ay


    Dy = det(Ay) = -4*25 - 2*1 = - 100 - 2 = -102.     <U>ANSWER</U>
</pre>

Solved.


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On Cramer's rule for solving systems of 2 equations in 2 unknowns see 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.


The most relevant / closest lessons are marked in the list as &nbsp;(*) &nbsp;and &nbsp;(**).


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>"