SOLUTION: Evaluate Dy. -4x + 7y = 1 25 = 2x + 5y

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Question 1162531: Evaluate Dy.
-4x + 7y = 1
25 = 2x + 5y
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            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".


Solution 

Step 1.  Write the system in the canonical form


    -4x + 7y =  1

     2x + 5y = 25



Step 2.  Write the coefficient matrix of the system


    A = %28matrix%282%2C2%2C++-4%2C7%2C++2%2C5%29%29



Step 3.  In matrix A, replace the second column by the right side vector

    
     Ay = %28matrix%282%2C2%2C+-4%2C1%2C++2%2C25%29%29.



Step 4.  Now Dy is the determinant of the matrix Ay


    Dy = det(Ay) = -4*25 - 2*1 = - 100 - 2 = -102.     ANSWER

Solved.

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On Cramer's rule for solving systems of 2 equations in 2 unknowns see the lessons
    - What is a matrix?
    - Determinant of a 2x2-matrix
    - HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule) (*)
    - Solving systems of linear equations in two unknowns using the Cramer's rule (**)
in this site.

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

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

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