document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003159>Question 1003159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without graphing, answer the following questions for the following linear system. \r<BR>\n" );
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document.write( "4x+3y=7<BR>\n" );
document.write( "28x+21y=5\r<BR>\n" );
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document.write( "A) is the system inconsistent or the equations dependent, or neither<BR>\n" );
document.write( "B) is the graph a pair of intersecting lines, a pair of parallel lines or one line<BR>\n" );
document.write( "C) does the system have one solution, no solution, or an infinite number of solutions.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619939 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=7 ALIGN=MIDDLE  ALT=\"4x%2B3y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%2B21y=5 ALIGN=MIDDLE  ALT=\"28x%2B21y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A) is the system inconsistent or the equations dependent, or neither\r<BR>\n" );
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document.write( "If slopes are different, system is independent.<BR>\n" );
document.write( "If slopes are same and intercepts are same, system is dependent.<BR>\n" );
document.write( "If slopes are same and intercepts are not the same, system is inconsistent.\r<BR>\n" );
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document.write( "so, we need to find slopes; write your equations in slope-intercept form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=7 ALIGN=MIDDLE  ALT=\"4x%2B3y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-4x%2B7 ALIGN=MIDDLE  ALT=\"3y=-4x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F3%29x%2B7%2F3 ALIGN=MIDDLE  ALT=\"y=-%284%2F3%29x%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "slope:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%284%2F3%29 ALIGN=MIDDLE  ALT=\"-%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y-intercept:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28x%2B21y=5 ALIGN=MIDDLE  ALT=\"28x%2B21y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21y=-28x%2B5 ALIGN=MIDDLE  ALT=\"21y=-28x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%2828%2F21%29x%2B5%2F21 ALIGN=MIDDLE  ALT=\"y=-%2828%2F21%29x%2B5%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F3%29x%2B5%2F21 ALIGN=MIDDLE  ALT=\"y=-%284%2F3%29x%2B5%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "slope:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%284%2F3%29 ALIGN=MIDDLE  ALT=\"-%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y-intercept:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F21 ALIGN=MIDDLE  ALT=\"5%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since slopes are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but intercepts are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > the same, system is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inconsistent ALIGN=MIDDLE  ALT=\"inconsistent\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "B) is the graph a pair of intersecting lines, a pair of parallel lines or one line\r<BR>\n" );
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document.write( "since slopes are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have a pair of parallel lines\r<BR>\n" );
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document.write( "C) does the system have one solution, no solution, or an infinite number of solutions.\r<BR>\n" );
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document.write( "if we have a pair of parallel lines, there will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+solution ALIGN=MIDDLE  ALT=\"+solution\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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