Question 1084436
.
Your step is wrong and leads you to <U>NOWHERE</U>. For correct steps see below.


Your prerequisite is the lesson

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

in this site. You must know its contents in order for to understand what follows.


<pre>
7x + 3y = 1
3x + 4y = 5


1.  Since you need to solve it using determinants, calculate the determinant of the coefficient matrix first:

    D = det {{{(matrix(2,2, 7,3, 3,4))}}} = 7*4 - 3*3 = 28 - 9 = 19.



2.  To solve for the first unknown, x, you need to modify the coefficient matrix by replacing it <U>first</U> column by the vector/column 
    of the constant terms of the right side; then calculate the determinant of the modified matrix:

    {{{D[x]}}} = det {{{(matrix(2,2, 1,3, 5,4))}}} = 1*4 - 3*5 = 4 - 15 = -11.

    Then the first unknown x is the ratio of the two determinants  x = {{{D[x]/D}}} = {{{-11/19}}}.


3.  To solve for the second unknown, y, you need to modify the coefficient matrix by replacing it <U>second</U> column by the vector/column 
    of the constant terms of the right side; then calculate the determinant of the modified matrix:

    {{{D[y]}}} = det {{{(matrix(2,2, 7,1, 3,5))}}} = 7*5 - 1*3 = 35 - 3 = 32.

    Then the second unknown, y, is the ratio of the two determinants  y = {{{D[y]/D}}} = {{{32/19}}}.


<U>Answer</U>.  x = {{{-11/19}}},  y = {{{32/19}}}.
</pre>

Again, see the lesson.

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

in this site.


The lesson is the part of this free of charge online textbook in ALGEBRA-I in this site

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


under the topic "<U>Systems of two linear equations in two unknowns</U>".



Another name for the <U>determinant method</U> is the <U>Cramer's rule</U>.


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>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-word-problems-by-reducing-them-to-systems-of-linear-equations-in-two-unknowns.lesson>Solving word problems by the Cramer's rule after reducing to systems of linear equations in two unknowns</A>, 

in this site.


Also, 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>"