document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936600>Question 936600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with these problems, I'm really confused. :( Thank you!\r<BR>\n" );
document.write( "\n" );
document.write( "How many solutions do the following systems of equations have? Justify your answer.\r<BR>\n" );
document.write( "\n" );
document.write( "a. -2x + 4y = 1, 3x - 6y = 9 \r<BR>\n" );
document.write( "\n" );
document.write( "b. x + y = 8, 2x + 2y = -1 \r<BR>\n" );
document.write( "\n" );
document.write( "c. y = (1/2)x - 4, x - 2y = 8<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570051 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=570051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are slopes of a pair of equations equal or unequal?<BR>\n" );
document.write( "Slopes equal, means the pair of lines either parallel or identical; if parallel but equations are not identical, then no point of intersection.  If equations of the lines are identical, then this just means that the pair is not really a pair, so just are the same line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If the slopes are unequal, then the pair intersect in exactly one point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Convert each pair of equations into the same form and simplify.  Suggested form could be slope-intercept.  You could choose standard form if you prefer, as long as you know what the parts of the equational form mean.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=8 ALIGN=MIDDLE  ALT=\"x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=-1 ALIGN=MIDDLE  ALT=\"2x%2B2y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplified into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=8 ALIGN=MIDDLE  ALT=\"x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=-1%2F2 ALIGN=MIDDLE  ALT=\"x%2By=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Same slope, but different constant value  for their right-hand members.  These lines are parallel and have no solution as a system.  They do not intersect. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );