document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115826>Question 115826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the method of substitution to solve the system of linear equations<BR>\n" );
document.write( "a)  x-y=8<BR>\n" );
document.write( "    x-y=-2\r<BR>\n" );
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document.write( "b)  2x+y=5<BR>\n" );
document.write( "    4x-3y=15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84290 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "a)  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=8 ALIGN=MIDDLE  ALT=\"x-y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=-2 ALIGN=MIDDLE  ALT=\"x-y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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++++1%5Cx+%2B+-1%5Cy+=+8%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+-2+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+-1%5Cy+=+8%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+-2+%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+=+8+-+-1%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+8+-+-1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F1+-+-1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+8%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=1%2A%288%2F1+-+-1%2Ay%2F1%29+%2B+-1%5Cy+=+-2 ALIGN=MIDDLE  ALT=\"1%2A%288%2F1+-+-1%2Ay%2F1%29+%2B+-1%5Cy+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=10=0. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F1+-+-1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+8%2F1+-+-1%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=18.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=18%2C+y=10=0+%29 ALIGN=MIDDLE  ALT=\"system%28+x=18%2C+y=10=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "b)  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=5 ALIGN=MIDDLE  ALT=\"2x%2By=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y=15 ALIGN=MIDDLE  ALT=\"4x-3y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+1%5Cy+=+5%2C%0D%0A++++4%5Cx+%2B+-3%5Cy+=+15+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+1%5Cy+=+5%2C%0D%0A++++4%5Cx+%2B+-3%5Cy+=+15+%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=2%2Ax+=+5+-+1%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+5+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F2+-+1%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+5%2F2+-+1%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=4%2A%285%2F2+-+1%2Ay%2F2%29+%2B+-3%5Cy+=+15 ALIGN=MIDDLE  ALT=\"4%2A%285%2F2+-+1%2Ay%2F2%29+%2B+-3%5Cy+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=-1. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F2+-+1%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+5%2F2+-+1%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=3.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=3%2C+y=-1+%29 ALIGN=MIDDLE  ALT=\"system%28+x=3%2C+y=-1+%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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