document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634169>Question 634169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Select any two integers between -12 & +12, which will become solutions to a system of two equations. Write two equations that have two integers as solutions. Solve your system of equations, using the addition and subtraction method, showing all 5 steps. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399429 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=399429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Pick an integer in the range <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -12\ <\ x\ <\ 12\">.  Set <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> equal to that integer.\r<BR>\n" );
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document.write( "Pick an integer in the range <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -12\ <\ y\ <\ 12\">.  Set <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> equal to that integer.\r<BR>\n" );
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document.write( "Then pick four other numbers to use for coefficients, they should be 4 different numbers and you can make some of them positive and some negtive.  I think you should pick small integers, but avoid zero.  I'm going to call these four numbers <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \alpha_1,\,\beta_1,\,\alpha_2,\,and\ \beta_2\"> for purposes of discussion.\r<BR>\n" );
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document.write( "Take the first of the coefficients (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \alpha_1\">) and multiply it by the value you chose for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">.  Take <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \beta_1\"> and multiply it by the value you chose for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">.  Add the two products and we'll call the sum <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \gamma_1\">.\r<BR>\n" );
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document.write( "Then write your first equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \alpha_1x\ +\ \beta_1y\ =\ \gamma_1\">\r<BR>\n" );
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document.write( "inserting the values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \alpha_1,\,\beta_1\,and\,\gamma_1\"> but leaving the variables <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> as variables.\r<BR>\n" );
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document.write( "Repeat the process using the same variable values and the other pair of coefficient values to calculate a new constant term, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \gamma_2\">.  Then write your second equation.\r<BR>\n" );
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document.write( "Write back and tell me what you came up with for a system of equations and we can discuss several possible strategies for solving the system.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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