document.write( "Question 1084436: need help making sure i have the right solution for:\r
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\n" ); document.write( "7x+3y=1
\n" ); document.write( "3x+4y=5\r
\n" ); document.write( "\n" ); document.write( "I have it reduced to 4x+ 19y= 32 is this the final answer?
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Algebra.Com's Answer #698539 by ikleyn(52864)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Your prerequisite is the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns using determinant\r
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document.write( "7x + 3y = 1\r\n" );
document.write( "3x + 4y = 5\r\n" );
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document.write( "1.  Since you need to solve it using determinants, calculate the determinant of the coefficient matrix first:\r\n" );
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document.write( "    D = det \"%28matrix%282%2C2%2C+7%2C3%2C+3%2C4%29%29\" = 7*4 - 3*3 = 28 - 9 = 19.\r\n" );
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document.write( "2.  To solve for the first unknown, x, you need to modify the coefficient matrix by replacing it first column by the vector/column \r\n" );
document.write( "    of the constant terms of the right side; then calculate the determinant of the modified matrix:\r\n" );
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document.write( "    \"D%5Bx%5D\" = det \"%28matrix%282%2C2%2C+1%2C3%2C+5%2C4%29%29\" = 1*4 - 3*5 = 4 - 15 = -11.\r\n" );
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document.write( "    Then the first unknown x is the ratio of the two determinants  x = \"D%5Bx%5D%2FD\" = \"-11%2F19\".\r\n" );
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document.write( "3.  To solve for the second unknown, y, you need to modify the coefficient matrix by replacing it second column by the vector/column \r\n" );
document.write( "    of the constant terms of the right side; then calculate the determinant of the modified matrix:\r\n" );
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document.write( "    \"D%5By%5D\" = det \"%28matrix%282%2C2%2C+7%2C1%2C+3%2C5%29%29\" = 7*5 - 1*3 = 35 - 3 = 32.\r\n" );
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document.write( "    Then the second unknown, y, is the ratio of the two determinants  y = \"D%5By%5D%2FD\" = \"32%2F19\".\r\n" );
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document.write( "Answer.  x = \"-11%2F19\",  y = \"32%2F19\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Again, see the lesson.\r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns using determinant\r
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\n" ); document.write( "\n" ); document.write( "The lesson is the part of this free of charge online textbook in ALGEBRA-I in this site\r
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\n" ); document.write( "\n" ); document.write( "under the topic \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Another name for the determinant method is the Cramer's rule.\r
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\n" ); document.write( "\n" ); document.write( "On Cramer's rule for solving systems of 2 equations in 2 unknowns see 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
\n" ); document.write( "\n" ); document.write( "    - Solving word problems by the Cramer's rule after reducing to systems of linear equations in two unknowns, \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
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
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