document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=411059>Question 411059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve this system of equations using substitution. Put your answer in ordered pair form, (x, y).\r<BR>\n" );
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document.write( "2x + 5y = 2<BR>\n" );
document.write( "   -3x - y = -3\r<BR>\n" );
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document.write( "Solve this system of equations using substitution. Put your answer in ordered pair form, (x, y).\r<BR>\n" );
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document.write( "    8x - y = 31<BR>\n" );
document.write( "    5x + 3y = 23\r<BR>\n" );
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document.write( "Solve this system of equations using substitution. Put your answer in ordered pair form, (x, y).\r<BR>\n" );
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document.write( "    2x + 6y = 24<BR>\n" );
document.write( "    5x - 2y = 9\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 #288944 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=288944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+5y+=+2 ALIGN=MIDDLE  ALT=\"2x+%2B+5y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x+-+y+=+-3 ALIGN=MIDDLE  ALT=\"-3x+-+y+=+-3\"   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+5%5Cy+=+2%2C%0D%0A++++-3%5Cx+%2B+-1%5Cy+=+-3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+5%5Cy+=+2%2C%0D%0A++++-3%5Cx+%2B+-1%5Cy+=+-3+%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+=+2+-+5%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+2+-+5%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F2+-+5%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+2%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=-3%2A%282%2F2+-+5%2Ay%2F2%29+%2B+-1%5Cy+=+-3 ALIGN=MIDDLE  ALT=\"-3%2A%282%2F2+-+5%2Ay%2F2%29+%2B+-1%5Cy+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=0. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F2+-+5%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+2%2F2+-+5%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=1.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=1%2C+y=0+%29 ALIGN=MIDDLE  ALT=\"system%28+x=1%2C+y=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "(1, 0)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+-y+=+31 ALIGN=MIDDLE  ALT=\"8x+-y+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+3y+=+23 ALIGN=MIDDLE  ALT=\"5x+%2B+3y+=+23\"   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++++8%5Cx+%2B+-1%5Cy+=+31%2C%0D%0A++++5%5Cx+%2B+3%5Cy+=+23+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++8%5Cx+%2B+-1%5Cy+=+31%2C%0D%0A++++5%5Cx+%2B+3%5Cy+=+23+%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=8%2Ax+=+31+-+-1%2Ay ALIGN=MIDDLE  ALT=\"8%2Ax+=+31+-+-1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+31%2F8+-+-1%2Ay%2F8 ALIGN=MIDDLE  ALT=\"x+=+31%2F8+-+-1%2Ay%2F8\"   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%2831%2F8+-+-1%2Ay%2F8%29+%2B+3%5Cy+=+23 ALIGN=MIDDLE  ALT=\"5%2A%2831%2F8+-+-1%2Ay%2F8%29+%2B+3%5Cy+=+23\"   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+=+31%2F8+-+-1%2Ay%2F8 ALIGN=MIDDLE  ALT=\"x+=+31%2F8+-+-1%2Ay%2F8\"   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=1+%29 ALIGN=MIDDLE  ALT=\"system%28+x=4%2C+y=1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "(4, 1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+6y+=+24 ALIGN=MIDDLE  ALT=\"2x+%2B+6y+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+-+2y+=+9 ALIGN=MIDDLE  ALT=\"5x+-+2y+=+9\"   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+6%5Cy+=+24%2C%0D%0A++++5%5Cx+%2B+-2%5Cy+=+9+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+6%5Cy+=+24%2C%0D%0A++++5%5Cx+%2B+-2%5Cy+=+9+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 6*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+=+24+-+6%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+24+-+6%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2F2+-+6%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+24%2F2+-+6%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%2824%2F2+-+6%2Ay%2F2%29+%2B+-2%5Cy+=+9 ALIGN=MIDDLE  ALT=\"5%2A%2824%2F2+-+6%2Ay%2F2%29+%2B+-2%5Cy+=+9\"   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+=+24%2F2+-+6%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+24%2F2+-+6%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=3+%29 ALIGN=MIDDLE  ALT=\"system%28+x=3%2C+y=3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "(3, 3)\r<BR>\n" );
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