Question 1121799
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<pre>
Use the Cramer's rule:


x = {{{det_x/det}}},


where det = determinant of the coefficient matrix  det {{{(matrix(2,2, 1,8, -7,7))}}} = 1*7 - 8*(-7) = 7 + 56 = 63,


det_x = determinant of the matrix obtained by replacing the first column of the coefficient matrix by the right side vector =


      = det {{{(matrix(2,2, -29,8,  -37,7))}}} = -29*7 - 8*(-37) = 93.


So,  x = {{{93/63}}} = {{{31/21}}}.


<U>Answer</U>.  {{{31/21}}}.
</pre>

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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.


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.