document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283529>Question 283529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two times a number plus three times another number equals 13. the sum of the two numbers is 7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205789 by </B><A HREF=/tutors/aboutme.mpl?userid=JenniferTutors><B>JenniferTutors(83)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JenniferTutors><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=JenniferTutors><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=205789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two times a number: 2x <BR>\n" );
document.write( "x = (unknown)a number<BR>\n" );
document.write( "Two times a number plus three times another number: 2x + 3y<BR>\n" );
document.write( "y = (unknown) another number<BR>\n" );
document.write( "Two times a number plus three times another number equals 13:<BR>\n" );
document.write( " 2x + 3y = 13\r<BR>\n" );
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document.write( "the sum of the two numbers is 7<BR>\n" );
document.write( "\"is\" usually can refer to equals<BR>\n" );
document.write( "the 2 unknown numbers are x & y, so:\r<BR>\n" );
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document.write( "x + y = 17\r<BR>\n" );
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document.write( "Now you have two equations:  2x + 3y = 13 & x + y = 7 \r<BR>\n" );
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document.write( "Here you can see that if you get one variable by itself in the second equation, you can place it into the first equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+7 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I have y by itself, by subtracting the x to the other side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x+%2B+7 ALIGN=MIDDLE  ALT=\"y+=+-x+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, you can place the y into the first equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+3y+=+13 ALIGN=MIDDLE  ALT=\"2x+%2B+3y+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+3%28-x+%2B+7%29+=+13 ALIGN=MIDDLE  ALT=\"2x+%2B+3%28-x+%2B+7%29+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Follow order of operations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+%28-3x%29+%2B+21+=+13 ALIGN=MIDDLE  ALT=\"2x+%2B+%28-3x%29+%2B+21+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I don't usually like to keep my problems like this, math books usually show you this way, honestly I think it's confusing, as long as you remember to keep the negative to the 3, look below I'll rewrite it so there isn't as many positive & neg signs:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+3x+%2B+21+=+13 ALIGN=MIDDLE  ALT=\"2x+-+3x+%2B+21+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next you subtract the like terms= x's :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+21+=+13 ALIGN=MIDDLE  ALT=\"-x+%2B+21+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To get x by itself, subtract the 21 :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+=+-21+%2B+13 ALIGN=MIDDLE  ALT=\"-x+=+-21+%2B+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+=+-8 ALIGN=MIDDLE  ALT=\"-x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You cannot leave variables in the negative this way, since a variable 'x'<BR>\n" );
document.write( "always has a one, but we usually don't write it '1x', Well to make the x positive we need to divide a negative 1 to both sides of the equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2F-1+=+-8%2F-1 ALIGN=MIDDLE  ALT=\"-x%2F-1+=+-8%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Negative/Negative equals Positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "Now you can place the x value into the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+7 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+%2B+y+=+7 ALIGN=MIDDLE  ALT=\"8+%2B+y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Get y by itself:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-8+%2B+7 ALIGN=MIDDLE  ALT=\"y+=+-8+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1 ALIGN=MIDDLE  ALT=\"y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have both of the values, x = 8, y = -1<BR>\n" );
document.write( "To Check, place the values into the first equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+3y+=+13 ALIGN=MIDDLE  ALT=\"2x+%2B+3y+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%288%29+%2B+3%28-1%29+=+13 ALIGN=MIDDLE  ALT=\"2%288%29+%2B+3%28-1%29+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+-+3+=+13 ALIGN=MIDDLE  ALT=\"16+-+3+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13+=+13 ALIGN=MIDDLE  ALT=\"13+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Checks out. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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