document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=405663>Question 405663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve 2x+3y=1 and -3x+y=15 by substitution?<BR>\n" );
document.write( "I have tried solving for the x and the y in the first probem but i getr frarctions and i dont think they are right.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286491 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=286491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y=1 ALIGN=MIDDLE  ALT=\"2x%2B3y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2By=15 ALIGN=MIDDLE  ALT=\"-3x%2By=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......... by substitution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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+3%5Cy+=+1%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+15+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+3%5Cy+=+1%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+15+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 3*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+=+1+-+3%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+1+-+3%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2+-+3%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+1%2F2+-+3%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=-3%2A%281%2F2+-+3%2Ay%2F2%29+%2B+1%5Cy+=+15 ALIGN=MIDDLE  ALT=\"-3%2A%281%2F2+-+3%2Ay%2F2%29+%2B+1%5Cy+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2+-+3%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+1%2F2+-+3%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=-4.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-4%2C+y=3+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-4%2C+y=3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );