document.write( "Question 457527: Can someone help me solve the solution of the system by using the elimination method to find the solution?\r
\n" ); document.write( "\n" ); document.write( "x + 5y = 20
\n" ); document.write( "-x + 8 = 19 \n" ); document.write( "

Algebra.Com's Answer #853411 by ikleyn(53538) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Can someone help me solve the solution of the system by using the elimination method to find the solution?
\n" ); document.write( "x + 5y = 20
\n" ); document.write( "-x +8y = 19
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        When somebody solves such a system by the elimination method, the major question\r
\n" ); document.write( "\n" ); document.write( "        is to choose a right strategy. The strategy which @mananth chooses in his solution,\r
\n" ); document.write( "\n" ); document.write( "        is difficult to call a rational or a reasonable. He makes tons of unnecessary calculations,\r
\n" ); document.write( "\n" ); document.write( "        which is easy to avoid if to use a rational strategy.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Your starting equations are  \r\n" );
document.write( "\r\n" );
document.write( "     x + 5y = 20     (1)\r\n" );
document.write( "    -x + 8y = 19     (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add the equations.  The terms 'x' of the first equation and '-x' of the second equation\r\n" );
document.write( "will cancel each other, opening the way to a short and clear straightforward solution\r\n" );
document.write( "\r\n" );
document.write( "         5y + 8y = 20 + 19,\r\n" );
document.write( "\r\n" );
document.write( "            13y  =    39\r\n" );
document.write( "\r\n" );
document.write( "              y  =    39/13 = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now from equation (1)  \r\n" );
document.write( "\r\n" );
document.write( "    x = 20 - 5y = 20 - 5*3 = 20 - 15 = 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  x = 5,  y = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  Substitute these values into equations to make sure that the answer is correct.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This way of solving by elimination is natural.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The way which @mananth promotes/uses in his post is (a) unnatural and (b) is a $\"highlight%28highlight%28wrong%29%29\"$ $\"highlight%28highlight%28way%29%29\"$ to teach.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/\/\/\/\/\/\/\/\/\/\/\/\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This my addition is specially for tutor @MathTherapy and for other tutors, who want to know the truth.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The truth is that @mananth solutions are not the solutions produced by a living person.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " They are the solutions produced by a computer code.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I started checking his solutions systematically somewhen in November-December of 2025.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "After checking approximately 70 of his solutions, I noticed repeating patterns in his solutions.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Very often these patterns were errors that a living person in healthy mind would never make.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It was a starting point for me to suggest that @mananth is a computer code.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "See my post under this link \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.434949.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.434949.html\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "where I first time formulated this my idea.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The more I submerged in his solutions the more I became sure that this is true.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now, after checking about 1000 of his solutions, I am 129% convinced in it.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The other side of this truth is/was that many hundreds (if not thousands) of the same type Math problems,
\n" ); document.write( "that were posted to this forum and solved by @mananth, were posted not by real students/visitors,
\n" ); document.write( "but were created and posted with the only goal to train this code in solving them, to demonstrate
\n" ); document.write( "the abilities of the code in solving such problems, to get checking from free of charge voluntary tutors
\n" ); document.write( "and, ultimately, to build a base of knowledge (= a base of solutions) for artificial intelligence.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );