document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=108989>Question 108989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by addition or subtraction.  If a unique solution does not exist, state whether the system is dependant or independent.<BR>\n" );
document.write( "10x+2y=7<BR>\n" );
document.write( "y=-5x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79555 by </B><A HREF=/tutors/aboutme.mpl?userid=mrkoje><B>mrkoje(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mrkoje><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=79555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello.\r<BR>\n" );
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document.write( "Eq (1)    10x + 2y = 7<BR>\n" );
document.write( "Eq (2)                  y = -5x + 3\r<BR>\n" );
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document.write( "Notice that if we add 5x to both sides of equation (2) we will get:\r<BR>\n" );
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document.write( "               5x + y = 3\r<BR>\n" );
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document.write( "Now forming our modified system of equations we get:\r<BR>\n" );
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document.write( "                 10x + 2y = 7<BR>\n" );
document.write( "                   5x +   y  = 3\r<BR>\n" );
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document.write( "Now here is the important part. To solve by addition or subtraction we will need to multiply Eq (2) by a some number that will let us clear out the \"x\" variable. \r<BR>\n" );
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document.write( "Here is what to do:\r<BR>\n" );
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document.write( "              Step 1.     Multiply Eq (2)  that is      2 * (5x + y = 3 )   which should give us  10x + 2y = 6. <BR>\n" );
document.write( "              Step 2.    Now we can subtract Eq (2) from (1).    <BR>\n" );
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document.write( "                                            10x + 2y  = 7<BR>\n" );
document.write( "                                    -      10x + 2y  = 6<BR>\n" );
document.write( "                                           _______________<BR>\n" );
document.write( "                                              0x  + 0y = 1             \r<BR>\n" );
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document.write( "(which is inconsistent since zero of something clearly can not equal one of something.)\r<BR>\n" );
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document.write( "Another way to look at the problem is with substitution. \r<BR>\n" );
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document.write( "For example in the original system:\r<BR>\n" );
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document.write( "                     10x + 2y =  7<BR>\n" );
document.write( "                                   y =  -5x +3\r<BR>\n" );
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document.write( "          The second equation is already solved for the variable \"y.\" We could just simply substitute that equation for the instance of Y in the first equation\r<BR>\n" );
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document.write( "                     10x + 2(-5x+3) = 7   \r<BR>\n" );
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document.write( "          Which expands to:\r<BR>\n" );
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document.write( "                     10x -10x + 6 = 7\r<BR>\n" );
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document.write( "          And that simplifies to:\r<BR>\n" );
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document.write( "                         6  =  7      (which is clearly not true) So we can see that the system in inconsistent. \r<BR>\n" );
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document.write( "Finally, a unique solution to this system is impossible. <BR>\n" );
document.write( "            \r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "          </SPAN>\n" );
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