document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157052>Question 1157052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system using the addition method.\r<BR>\n" );
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document.write( "1.11x-5y=10<BR>\n" );
document.write( "  13x-7y=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779846 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "    11x - 5y = 10     (1)\r\n" );
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document.write( "    13x - 7y =  2     (2)\r\n" );
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document.write( "The idea of this method is to multiply each equation by some number in such a way\r\n" );
document.write( "to make the coefficients at some variable EQUAL (or OPPOSITE).\r\n" );
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document.write( "Then by subtracting equations, we can DELETE this variable in the resulting equation.\r\n" );
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document.write( "So, we will get in this way SINGLE equation with ONLY ONE unknown, which is easy to solve.\r\n" );
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document.write( "Looking into the given equations, you see that the better and the simplest way is to multiply \r\n" );
document.write( "first equation by 7 and the second equation by 5.\r\n" );
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document.write( "You will get then  these two equations\r\n" );
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document.write( "    77x - 35y = 70     (3)\r\n" );
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document.write( "    65x - 35y = 10     (4)\r\n" );
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document.write( "Do you see these terms \"35y\" in each equations ?  They are exactly that we were going to provide (and we provided them (!) ).\r\n" );
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document.write( "Now from equation (3) subtract equation (4). The terms \"-35y\" will cancel each other, \r\n" );
document.write( "and you will get ONE SINGLE equation for the unknown x ONLY (!)\r\n" );
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document.write( "    77x - 65x = 70 - 10.\r\n" );
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document.write( "Simplify and solve it, as the equation with only one unknown x\r\n" );
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document.write( "    12x       = 60.\r\n" );
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document.write( "     x        = 60/12 = 5.\r\n" );
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document.write( "The last step is to substitute this value of x into EITHER of the two original equations.\r\n" );
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document.write( "You will get then an equation for \"y\" only, and you should solve it to get y.\r\n" );
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document.write( "Do it on your own.\r\n" );
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document.write( "I completed my explanations.\r<BR>\n" );
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document.write( "Now I ask you &nbsp;&nbsp;1) &nbsp;if you do understand everything in my post,\r<BR>\n" );
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document.write( "and &nbsp;&nbsp;2) &nbsp;please inform me if you there able to complete the solution.\r<BR>\n" );
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document.write( "If you will post to me, &nbsp;PLEASE &nbsp;refer to the problem's &nbsp;ID number &nbsp;1157052;\r<BR>\n" );
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document.write( "otherwise, &nbsp;I will not know to which problem your message does relate.\r<BR>\n" );
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document.write( "===============\r<BR>\n" );
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document.write( "In this site, there is the lesson, explaining this technology in all details.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF= http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-system-of-two-eqns-by-the-Subst-method.lesson>Solution of the linear system of two equations in two unknowns by the Substitution method</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF= http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of the linear system of two equations in two unknowns by the Elimination method</A> \r<BR>\n" );
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document.write( "It is the SECOND lesson in this short list.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic \"<U>Systems of two linear equations in two unknowns</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( "It is my response to your question :   &nbsp;&nbsp;x = 5, &nbsp;y = 9.\r<BR>\n" );
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document.write( "You may check it by substituting the values into original equations.\r<BR>\n" );
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