document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124262>Question 124262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A KELLY BOUGHT 2 TACOS AND 3 ENCHILLADAS.  FRED BOUGHT 3 TACOS AND 5 ENCHILLADAS.  ONE BILL IS $7.80 THE OTHER IS $12.70.  HOW MUCH WAS EACH TACO AND ECHILLADA ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91065 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2t+3e=7.8<BR>\n" );
document.write( "3t+5e=12.7<BR>\n" );
document.write( ".<BR>\n" );
document.write( "tacos cost $.90 and enchaladas $2.00<BR>\n" );
document.write( "Ed<BR>\n" );
document.write( ".<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=change_this_name6744.solver>Linear Systems by Addition</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>We'll solve the system:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2At+%2B+3%2Ae+=+7.8 ALIGN=MIDDLE  ALT=\"2%2At+%2B+3%2Ae+=+7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2At+%2B+5%2Ae+=+12.7 ALIGN=MIDDLE  ALT=\"3%2At+%2B+5%2Ae+=+12.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 3 as our coefficient for x, to get  -2 we have to multiply all terms of the second equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equal to -0.666666666666667.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Multiplying, we get on our second equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A-0.666666666666667%29t+%2B+%285%2A-0.666666666666667%29e+=+12.7%2A-0.666666666666667 ALIGN=MIDDLE  ALT=\"%283%2A-0.666666666666667%29t+%2B+%285%2A-0.666666666666667%29e+=+12.7%2A-0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2At+%2B+-3.33333333333333%2Ae+=+-8.46666666666667 ALIGN=MIDDLE  ALT=\"-2%2At+%2B+-3.33333333333333%2Ae+=+-8.46666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Adding both equations we get:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B-2%29t+%2B+%283%2B-3.33333333333333%29e+=+%287.8%2B-8.46666666666667%29 ALIGN=MIDDLE  ALT=\"%282%2B-2%29t+%2B+%283%2B-3.33333333333333%29e+=+%287.8%2B-8.46666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since 2 and -2 cancel out, we have a linear equation:Therefore, we know that e = 2.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plugging that in into the first equation gives us:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2At+%2B+3%2Ae+=+7.8 ALIGN=MIDDLE  ALT=\"2%2At+%2B+3%2Ae+=+7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2At+%2B+3%2A2+=+7.8 ALIGN=MIDDLE  ALT=\"2%2At+%2B+3%2A2+=+7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2At+%2B+5.99999999999999+=+7.8 ALIGN=MIDDLE  ALT=\"2%2At+%2B+5.99999999999999+=+7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2At+=+7.8+-+5.99999999999999 ALIGN=MIDDLE  ALT=\"2%2At+=+7.8+-+5.99999999999999\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%287.8+-+5.99999999999999%29%2F2 ALIGN=MIDDLE  ALT=\"t+=+%287.8+-+5.99999999999999%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.80000000000001%2F2 ALIGN=MIDDLE  ALT=\"t+=+1.80000000000001%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0.900000000000004 ALIGN=MIDDLE  ALT=\"t+=+0.900000000000004\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Therefore, our answer is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+t=0.900000000000004%2C+e=2+%29 ALIGN=MIDDLE  ALT=\"system%28+t=0.900000000000004%2C+e=2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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