document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443108>Question 443108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following systems of equations x + 5y=2 3x + 19=y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305651 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Get in this form ax+by =c<BR>\n" );
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document.write( "x+5y=2<BR>\n" );
document.write( "3x-y=-19\r<BR>\n" );
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document.write( "Multiply the the first by -3\r<BR>\n" );
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document.write( "-3x -15y =-6<BR>\n" );
document.write( "3x -y  = -19\r<BR>\n" );
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document.write( "Add the two together\r<BR>\n" );
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document.write( "0  + -16y = -25\r<BR>\n" );
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document.write( "y = 25/16\r<BR>\n" );
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document.write( "x + 5(25/16) = 2<BR>\n" );
document.write( "x + 125/16 = 2<BR>\n" );
document.write( "x = 32/16 - 125/16<BR>\n" );
document.write( "x = -93/16\r<BR>\n" );
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document.write( "x = -93/16  y= 25/16\r<BR>\n" );
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document.write( "Let's check this:<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+5%5Cy+=+2%2C%0D%0A++++3%5Cx+%2B+-1%5Cy+=+-19+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+5%5Cy+=+2%2C%0D%0A++++3%5Cx+%2B+-1%5Cy+=+-19+%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=1%2Ax+=+2+-+5%2Ay ALIGN=MIDDLE  ALT=\"1%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%2F1+-+5%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+2%2F1+-+5%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=3%2A%282%2F1+-+5%2Ay%2F1%29+%2B+-1%5Cy+=+-19 ALIGN=MIDDLE  ALT=\"3%2A%282%2F1+-+5%2Ay%2F1%29+%2B+-1%5Cy+=+-19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=1.5625. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F1+-+5%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+2%2F1+-+5%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=-5.8125.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=-5.8125%2C+y=1.5625+%29 ALIGN=MIDDLE  ALT=\"system%28+x=-5.8125%2C+y=1.5625+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Which in decimal form is the same as before.<BR>\n" );
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