document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221279>Question 221279</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations by graphing. Then classify the system.<BR>\n" );
document.write( "3x+ y=15<BR>\n" );
document.write( "4x+5y=-13<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 #166010 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=166010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations by graphing. Then classify the system.\r<BR>\n" );
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document.write( "3x+ y=15<BR>\n" );
document.write( "4x+5y=-13\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++++3%5Cx+%2B+1%5Cy+=+15%2C%0D%0A++++4%5Cx+%2B+5%5Cy+=+-13+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++3%5Cx+%2B+1%5Cy+=+15%2C%0D%0A++++4%5Cx+%2B+5%5Cy+=+-13+%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=3%2Ax+=+15+-+1%2Ay ALIGN=MIDDLE  ALT=\"3%2Ax+=+15+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15%2F3+-+1%2Ay%2F3 ALIGN=MIDDLE  ALT=\"x+=+15%2F3+-+1%2Ay%2F3\"   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%2815%2F3+-+1%2Ay%2F3%29+%2B+5%5Cy+=+-13 ALIGN=MIDDLE  ALT=\"4%2A%2815%2F3+-+1%2Ay%2F3%29+%2B+5%5Cy+=+-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=-9. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15%2F3+-+1%2Ay%2F3 ALIGN=MIDDLE  ALT=\"x+=+15%2F3+-+1%2Ay%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=8.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=8%2C+y=-9+%29 ALIGN=MIDDLE  ALT=\"system%28+x=8%2C+y=-9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The linear system of equations is independent and has a unique solution intersecting at a point (8,-9). \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 </SPAN>\n" );
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