document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=701519>Question 701519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this linear equation using substitution\r<BR>\n" );
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document.write( "1/2x + 2/3y = 1<BR>\n" );
document.write( "1/4x - 1/3y = 5/2\r<BR>\n" );
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document.write( "Thank you.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432521 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=432521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's not perfectly clear to me, but<BR>\n" );
document.write( "I assume that the problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%281%2F2%29x+%2B+%282%2F3%29y+=+1%2C%281%2F4%29x+-+%281%2F3%29y+=+5%2F2%29 ALIGN=MIDDLE  ALT=\"system%28%281%2F2%29x+%2B+%282%2F3%29y+=+1%2C%281%2F4%29x+-+%281%2F3%29y+=+5%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and I'll solve that.<BR>\n" );
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document.write( "If I had a choice, I would not solve that system by substitution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x+-+%281%2F3%29y+=+5%2F2+ ALIGN=MIDDLE  ALT=\"%281%2F4%29x+-+%281%2F3%29y+=+5%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x+=+%281%2F3%29y%2B5%2F2+ ALIGN=MIDDLE  ALT=\"%281%2F4%29x+=+%281%2F3%29y%2B5%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2F3%29y%2B10 ALIGN=MIDDLE  ALT=\"x=%284%2F3%29y%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29y%2B10 ALIGN=MIDDLE  ALT=\"%284%2F3%29y%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x+%2B+%282%2F3%29y+=+1 ALIGN=MIDDLE  ALT=\"%281%2F2%29x+%2B+%282%2F3%29y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%284%2F3%29y%2B10%29+%2B+%282%2F3%29y+=+1 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28%284%2F3%29y%2B10%29+%2B+%282%2F3%29y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29y%2B5%2B+%282%2F3%29y+=+1 ALIGN=MIDDLE  ALT=\"%282%2F3%29y%2B5%2B+%282%2F3%29y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29y=1-5 ALIGN=MIDDLE  ALT=\"%284%2F3%29y=1-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29y=-4 ALIGN=MIDDLE  ALT=\"%284%2F3%29y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%284%2F3%29y=-4%283%2F4%29 ALIGN=MIDDLE  ALT=\"%283%2F4%29%284%2F3%29y=-4%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then, substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29 ALIGN=MIDDLE  ALT=\"%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2F3%29y%2B10 ALIGN=MIDDLE  ALT=\"x=%284%2F3%29y%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2F3%29%28-3%29%2B10 ALIGN=MIDDLE  ALT=\"x=%284%2F3%29%28-3%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2B10 ALIGN=MIDDLE  ALT=\"x=-4%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If I could choose how to solve it,<BR>\n" );
document.write( "I would first transform the equations,<BR>\n" );
document.write( "so as to get equivalent equations without fractions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x+%2B+%282%2F3%29y+=+1 ALIGN=MIDDLE  ALT=\"%281%2F2%29x+%2B+%282%2F3%29y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=6 ALIGN=MIDDLE  ALT=\"3x%2B4y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplying everything times 6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x+-+%281%2F3%29y+=+5%2F2+ ALIGN=MIDDLE  ALT=\"%281%2F4%29x+-+%281%2F3%29y+=+5%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4y=30 ALIGN=MIDDLE  ALT=\"3x-4y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplying everything times 12)<BR>\n" );
document.write( "Then I would add both equations to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=36 ALIGN=MIDDLE  ALT=\"6x=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I would also subtract the second equation from the first one to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y=-24 ALIGN=MIDDLE  ALT=\"8y=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF THE PROBLEM WAS<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%281%2F2x+%2B+2%2F3y+=+1%2C1%2F4x+-+1%2F3y+=+5%2F2+%29 ALIGN=MIDDLE  ALT=\"system%281%2F2x+%2B+2%2F3y+=+1%2C1%2F4x+-+1%2F3y+=+5%2F2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "That's the same as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%281%2F2%29%281%2Fx%29+%2B+%282%2F3%29%281%2Fy%29+=+1%2C%281%2F4%29%281%2Fx%29+-+%281%2F3%29%281%2Fy%29+=+5%2F2+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That could be solve the same way for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fy ALIGN=MIDDLE  ALT=\"1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx=6 ALIGN=MIDDLE  ALT=\"1%2Fx=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fy=-3 ALIGN=MIDDLE  ALT=\"1%2Fy=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then the solutions would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F6 ALIGN=MIDDLE  ALT=\"x=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F3 ALIGN=MIDDLE  ALT=\"y=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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