document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213715>Question 213715</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0075525984/algebrahomeworkh>MATHPOWER 11</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve by elimination. Check each solution.<BR>\n" );
document.write( "21. 6x-5y=-3<BR>\n" );
document.write( "    2y-9x=-1\r<BR>\n" );
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document.write( "Please help me out ive been stuck on this one for a while! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161449 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=161449\">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=6x-5y=-3 ALIGN=MIDDLE  ALT=\"6x-5y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y-9x=-1 ALIGN=MIDDLE  ALT=\"2y-9x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1.  Rearrange to align the x and y terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-5y=-3 ALIGN=MIDDLE  ALT=\"6x-5y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply by 3  to both sides to get 18x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x%2B2y=-1 ALIGN=MIDDLE  ALT=\"-9x%2B2y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply by 2 to both sides to get -18x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-15y=-9 ALIGN=MIDDLE  ALT=\"18x-15y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Eq 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18x%2B4y=-2 ALIGN=MIDDLE  ALT=\"-18x%2B4y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Eq 2\r<BR>\n" );
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document.write( "Step 2.  Adding above equations Eq 1 and Eq 2 yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11y=-11 ALIGN=MIDDLE  ALT=\"-11y=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or y=1\r<BR>\n" );
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document.write( "Step 3.  Substitute y=1 into 6x-5y=-3 yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-5%281%29=-3 ALIGN=MIDDLE  ALT=\"6x-5%281%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=-3%2B5 ALIGN=MIDDLE  ALT=\"6x=-3%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2F6=2%2F6 ALIGN=MIDDLE  ALT=\"6x%2F6=2%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Step 5.  To verify, the following will solve the linear systems using substitution.\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++++6%5Cx+%2B+-5%5Cy+=+-3%2C%0D%0A++++-9%5Cx+%2B+2%5Cy+=+-1+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++6%5Cx+%2B+-5%5Cy+=+-3%2C%0D%0A++++-9%5Cx+%2B+2%5Cy+=+-1+%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=6%2Ax+=+-3+-+-5%2Ay ALIGN=MIDDLE  ALT=\"6%2Ax+=+-3+-+-5%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F6+-+-5%2Ay%2F6 ALIGN=MIDDLE  ALT=\"x+=+-3%2F6+-+-5%2Ay%2F6\"   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=-9%2A%28-3%2F6+-+-5%2Ay%2F6%29+%2B+2%5Cy+=+-1 ALIGN=MIDDLE  ALT=\"-9%2A%28-3%2F6+-+-5%2Ay%2F6%29+%2B+2%5Cy+=+-1\"   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+=+-3%2F6+-+-5%2Ay%2F6 ALIGN=MIDDLE  ALT=\"x+=+-3%2F6+-+-5%2Ay%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=0.333333333333333.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=0.333333333333333%2C+y=1+%29 ALIGN=MIDDLE  ALT=\"system%28+x=0.333333333333333%2C+y=1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Step 6.  Same result...the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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