document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26306>Question 26306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems by using either addition or substitution.  If a unique solution does not exist, state whether the system is dependent or inconsistent.\r<BR>\n" );
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document.write( "10x + 2y = 7<BR>\n" );
document.write( "      y=-5x+3\r<BR>\n" );
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document.write( "Please help me.\r<BR>\n" );
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document.write( "Thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14286 by </B><A HREF=/tutors/aboutme.mpl?userid=Alwayscheerful><B>Alwayscheerful(414)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alwayscheerful><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\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++++10%5Cx+%2B+2%5Cy+=+7%2C%0D%0A++++5%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++10%5Cx+%2B+2%5Cy+=+7%2C%0D%0A++++5%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 2*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax+=+7+-+2%2Ay ALIGN=MIDDLE  ALT=\"10%2Ax+=+7+-+2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F10+-+2%2Ay%2F10 ALIGN=MIDDLE  ALT=\"x+=+7%2F10+-+2%2Ay%2F10\"   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%287%2F10+-+2%2Ay%2F10%29+%2B+1%5Cy+=+3 ALIGN=MIDDLE  ALT=\"5%2A%287%2F10+-+2%2Ay%2F10%29+%2B+1%5Cy+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=1/2=0. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F10+-+2%2Ay%2F10 ALIGN=MIDDLE  ALT=\"x+=+7%2F10+-+2%2Ay%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=0.5.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=0.5%2C+y=1%2F2=0+%29 ALIGN=MIDDLE  ALT=\"system%28+x=0.5%2C+y=1%2F2=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "OR\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.solver>Linear System solver (using determinant)</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++++10%5Cx+%2B+2%5Cy+=+7%2C%0D%0A++++5%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++10%5Cx+%2B+2%5Cy+=+7%2C%0D%0A++++5%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ax+%2B+a%5B12%5D%2Ay+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ax+%2B+a%5B22%5D%2Ay+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++x+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++y+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "Hope this helps! </SPAN>\n" );
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