document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224440>Question 224440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have?\r<BR>\n" );
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document.write( "How many solutions does the following equations have?<BR>\n" );
document.write( "8x+4y=8<BR>\n" );
document.write( "2x-2y=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167690 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=167690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have?  None, One, and Many\r<BR>\n" );
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document.write( "How many solutions does the following equations have?  One. The lines intersect at one point as shown below at (0,2)\r<BR>\n" );
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document.write( "8x+4y=8<BR>\n" );
document.write( "2x-2y=-4\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++++8%5Cx+%2B+4%5Cy+=+8%2C%0D%0A++++2%5Cx+%2B+-2%5Cy+=+-4+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++8%5Cx+%2B+4%5Cy+=+8%2C%0D%0A++++2%5Cx+%2B+-2%5Cy+=+-4+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 4*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ax+=+8+-+4%2Ay ALIGN=MIDDLE  ALT=\"8%2Ax+=+8+-+4%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F8+-+4%2Ay%2F8 ALIGN=MIDDLE  ALT=\"x+=+8%2F8+-+4%2Ay%2F8\"   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=2%2A%288%2F8+-+4%2Ay%2F8%29+%2B+-2%5Cy+=+-4 ALIGN=MIDDLE  ALT=\"2%2A%288%2F8+-+4%2Ay%2F8%29+%2B+-2%5Cy+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=2. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F8+-+4%2Ay%2F8 ALIGN=MIDDLE  ALT=\"x+=+8%2F8+-+4%2Ay%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=0.<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%2C+y=2+%29 ALIGN=MIDDLE  ALT=\"system%28+x=0%2C+y=2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<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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