document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57309>Question 57309</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1592009425/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 1. Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations. \r<BR>\n" );
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document.write( "Let p = the cost of one pear \r<BR>\n" );
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document.write( "Let a = the cost of one apple\r<BR>\n" );
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document.write( "a. Write a system of equations that can be used to determine the cost of pears and apples. <BR>\n" );
document.write( " Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer. \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 #39012 by </B><A HREF=/tutors/aboutme.mpl?userid=hayek><B>hayek(51)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hayek><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=39012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We'll use P to be the price of one pear and A to be the price of one apple:\r<BR>\n" );
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document.write( "First Equation: 6*P + 3*A = 3.90<BR>\n" );
document.write( "Second Equation 2*P + 5*A = 3.30\r<BR>\n" );
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document.write( "Solve first eq. for P:<BR>\n" );
document.write( "6P=3.90-3A<BR>\n" );
document.write( "P=3.90/6 - 3A/6\r<BR>\n" );
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document.write( "Plug into second equation:<BR>\n" );
document.write( "2*(3.90/6 - 3A/6) +5A = 3.30\r<BR>\n" );
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document.write( "Simplify:<BR>\n" );
document.write( "1.3 - 6A/6 + 5A = 3.30<BR>\n" );
document.write( "1.3 -A + 5A = 3.30<BR>\n" );
document.write( "1.3 + 4A = 3.30<BR>\n" );
document.write( "4A = 3.30-1.30<BR>\n" );
document.write( "4A = 2<BR>\n" );
document.write( "A = 0.5\r<BR>\n" );
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document.write( "So each apple (A) is $0.50\r<BR>\n" );
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document.write( "Plug into Eq 1 to find P:  6*P + 3*(.5)=3.90\r<BR>\n" );
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document.write( "6P + 1.5 = 3.90<BR>\n" );
document.write( "6P =3.90-1.5<BR>\n" );
document.write( "6P = 2.4<BR>\n" );
document.write( "P = $.40\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++6%5Cp+%2B+3%5Ca+=+3.9%2C%0D%0A++++2%5Cp+%2B+5%5Ca+=+3.3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++6%5Cp+%2B+3%5Ca+=+3.9%2C%0D%0A++++2%5Cp+%2B+5%5Ca+=+3.3+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ap+%2B+a%5B12%5D%2Aa+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ap+%2B+a%5B22%5D%2Aa+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++p+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++a+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++p+=+%283.9%2A5+-+3.3%2A3%29%2F%286%2A5-2%2A3%29+=+0.4%2C%0D%0A++++++a+=+%286%2A3.3+-+2%2A3.9%29%2F%286%2A5-2%2A3%29+=+0.5%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (p=0.4, a=0.5}<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
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