document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224017>Question 224017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of twice a first number and five times a secod number is 92. If the second number is subtracted from five times the first number the result is 14. find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167368 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of twice a first number and five times a second number is 92. If the second number is subtracted from five times the first number the result is 14. Find the numbers.\r<BR>\n" );
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document.write( "Step 1.  Let x be first number.\r<BR>\n" );
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document.write( "Step 2.  Let y be the second number.\r<BR>\n" );
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document.write( "Step 3.  Let 2x+5y=92 since the sum of twice a first number and five times a second number is 92.\r<BR>\n" );
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document.write( "Step 4.  Also, 5x-y=14 since the second number is subtracted from five times the first number the result is 14.\r<BR>\n" );
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document.write( "Step 5.  We have a system of equations given by Steps 3 and 4.\r<BR>\n" );
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document.write( "2x+5y=92<BR>\n" );
document.write( "5x-y=14\r<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=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</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++++2%5Cx+%2B+5%5Cy+=+92%2C%0D%0A++++5%5Cx+%2B+-1%5Cy+=+14+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+5%5Cy+=+92%2C%0D%0A++++5%5Cx+%2B+-1%5Cy+=+14+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 5*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+=+92+-+5%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+92+-+5%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+92%2F2+-+5%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+92%2F2+-+5%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%2892%2F2+-+5%2Ay%2F2%29+%2B+-1%5Cy+=+14 ALIGN=MIDDLE  ALT=\"5%2A%2892%2F2+-+5%2Ay%2F2%29+%2B+-1%5Cy+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=16. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+92%2F2+-+5%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+92%2F2+-+5%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=6.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=6%2C+y=16+%29 ALIGN=MIDDLE  ALT=\"system%28+x=6%2C+y=16+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Step 6.  ANSWER:  The numbers are 6 and 16.\r<BR>\n" );
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document.write( "I hope the above steps and explanation were helpful. \r<BR>\n" );
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document.write( "For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for \r<BR>\n" );
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document.write( "Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry. \r<BR>\n" );
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document.write( "Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.\r<BR>\n" );
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document.write( "Respectfully, <BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV\r<BR>\n" );
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document.write( " </SPAN>\n" );
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