document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143307>Question 143307</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618250182/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear system\r<BR>\n" );
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document.write( "y = x + 7<BR>\n" );
document.write( "2x + 3y = 31    (hint: substitution) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104423 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=104423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem is already solved for y in the first equation. Put that into the second and solve...\r<BR>\n" );
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document.write( "ie 2x + 3y = 31<BR>\n" );
document.write( "         ^substitute x+7 for y<BR>\n" );
document.write( "  2x +  3(x+7)=31<BR>\n" );
document.write( " 5x=10<BR>\n" );
document.write( "  x=2\r<BR>\n" );
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document.write( "If x=2, y must be 9.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "x+7-->2+7=9  yes<BR>\n" );
document.write( "2x+3y=2(2)+3(9)=4+27=31  yes\r<BR>\n" );
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document.write( "And here is how this site's solver would do it:<BR>\n" );
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_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++++1%5Cx+%2B+-1%5Cy+=+-7%2C%0D%0A++++2%5Cx+%2B+3%5Cy+=+31+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+-1%5Cy+=+-7%2C%0D%0A++++2%5Cx+%2B+3%5Cy+=+31+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving -1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+-7+-+-1%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+-7+-+-1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7%2F1+-+-1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+-7%2F1+-+-1%2Ay%2F1\"   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=2%2A%28-7%2F1+-+-1%2Ay%2F1%29+%2B+3%5Cy+=+31 ALIGN=MIDDLE  ALT=\"2%2A%28-7%2F1+-+-1%2Ay%2F1%29+%2B+3%5Cy+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=9. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7%2F1+-+-1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+-7%2F1+-+-1%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=2.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=2%2C+y=9+%29 ALIGN=MIDDLE  ALT=\"system%28+x=2%2C+y=9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " </SPAN>\n" );
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