document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214684>Question 214684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve linear system<BR>\n" );
document.write( "-4x-3y=-27<BR>\n" );
document.write( "-4x+4y=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162117 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=162117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve linear system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-3y=-27 ALIGN=MIDDLE  ALT=\"-4x-3y=-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2B4y=8 ALIGN=MIDDLE  ALT=\"-4x%2B4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation B\r<BR>\n" );
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document.write( "Step 1.  Subtract Equation B from Equation A to get rid of x terms  to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7y=-35 ALIGN=MIDDLE  ALT=\"-7y=-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2.  Divide by -7 to both sides to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7y%2F7=-35%2F-7 ALIGN=MIDDLE  ALT=\"-7y%2F7=-35%2F-7\"   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=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  Substitute y=5 into one of the equation to get x\r<BR>\n" );
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document.write( "{{-4x-3(5)=-27}}}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-15=-27 ALIGN=MIDDLE  ALT=\"-4x-15=-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  Add 15 to both sides to get x-terms on the left side and numbers on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-15%2B15=-27%2B15 ALIGN=MIDDLE  ALT=\"-4x-15%2B15=-27%2B15\"   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=-4x=-12 ALIGN=MIDDLE  ALT=\"-4x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  Divide by -4 to both sides of equation to get x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2F-4=-12%2F-4 ALIGN=MIDDLE  ALT=\"-4x%2F-4=-12%2F-4\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  ANSWER:  Solution is  x=3 and y=5\r<BR>\n" );
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document.write( "We can also solve the equation 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++++-4%5Cx+%2B+-3%5Cy+=+-27%2C%0D%0A++++-4%5Cx+%2B+4%5Cy+=+8+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++-4%5Cx+%2B+-3%5Cy+=+-27%2C%0D%0A++++-4%5Cx+%2B+4%5Cy+=+8+%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=-4%2Ax+=+-27+-+-3%2Ay ALIGN=MIDDLE  ALT=\"-4%2Ax+=+-27+-+-3%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-27%2F-4+-+-3%2Ay%2F-4 ALIGN=MIDDLE  ALT=\"x+=+-27%2F-4+-+-3%2Ay%2F-4\"   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%28-27%2F-4+-+-3%2Ay%2F-4%29+%2B+4%5Cy+=+8 ALIGN=MIDDLE  ALT=\"-4%2A%28-27%2F-4+-+-3%2Ay%2F-4%29+%2B+4%5Cy+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=5. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-27%2F-4+-+-3%2Ay%2F-4 ALIGN=MIDDLE  ALT=\"x+=+-27%2F-4+-+-3%2Ay%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=3.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=3%2C+y=5+%29 ALIGN=MIDDLE  ALT=\"system%28+x=3%2C+y=5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Same result as before.\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 on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And 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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