document.write( "Question 1114252: When using Cramers Rule for a particular system: https://imgur.com/bG0348i\r
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Algebra.Com's Answer #729235 by ikleyn(53943) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1.  When solving system by the Cramer's method (=Cramer's rule), \r\n" );
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document.write( "    the denominator in the formula is the determinant of the matrix of the system.\r\n" );
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document.write( "    So, from the referred picture, the matrix of the system is  .\r\n" );
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document.write( "    When solving system by the Cramer's method (=Cramer's rule),\r\n" );
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document.write( "    the numerator in the formula for x is is the determinant of the matrix,\r\n" );
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document.write( "    whose first vertical column is the vector of the right hand side.\r\n" );
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document.write( "    Therefore, the system of equations is THIS:\r\n" );
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document.write( "        3x + 5y = 33,\r\n" );
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document.write( "        5x + 7y = 51.\r\n" );
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document.write( "2.  The determinant of the major matrix is 3*7 - 5*5 = 21-25 = -4.\r\n" );
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document.write( "    It is the denominator in formulas for x and y, according to the Cramer's rule.\r\n" );
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document.write( "    The determinant in the numerator for the formula for y  is\r\n" );
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document.write( "         det  = 3*51-5*33 = -12.\r\n" );
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document.write( "3.  The determinant in the numerator for the formula for x  is\r\n" );
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document.write( "         det  = 33*7-5*51 = -24.\r\n" );
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document.write( "    Therefore, the solution to the system is x =  = 6,  y =  = 3.\r\n" );
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document.write( "     Check:  1-st eq.: 3*6 + 5*3 = 33    ! Correct !\r\n" );
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document.write( "             2-nd eq.: 5*6 + 7*3 = 51    ! Correct !\r\n" );
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document.write( "4.  The values of x and y (= the solution to the system)  are x= 6,  y= 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I answered all the questions.\r
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\n" ); document.write( "\n" ); document.write( "If you want to learn everything about the Cramer's rule related to 2x2-systems of equations,\r
\n" ); document.write( "\n" ); document.write( "read the lessons \r
\n" ); document.write( "\n" ); document.write( "    - What is a matrix?,\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule),\r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of linear equations in two unknowns using the Cramer's rule,\r
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\n" ); document.write( "\n" ); document.write( "You have rare opportunity to learn this theory and to look into examples from the best source. Do not miss it !\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "     \"2x2-Matrices, determinants, Cramer's rule for systems in two unknowns\" \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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