document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184719>Question 184719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. \r<BR>\n" );
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document.write( "-	Determine how many solutions exist<BR>\n" );
document.write( "-	Use either elimination or substitution to find the solutions (if any)<BR>\n" );
document.write( "-	Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection\r<BR>\n" );
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document.write( " 0.2x + 0.4y = 1.7  and  8.3x - 6.3y = -4.3\r<BR>\n" );
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document.write( "need help desperately! Thank you.<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 #138670 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> - Determine how many solutions exist<BR>\n" );
document.write( "- Use either elimination or substitution to find the solutions (if any) <BR>\n" );
document.write( "Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection<BR>\n" );
document.write( "0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "get rid of the decimals, multiply both equations by 10, results<BR>\n" );
document.write( "2x + 4y = 17 <BR>\n" );
document.write( "83x - 63y = -43<BR>\n" );
document.write( ";<BR>\n" );
document.write( "We will use elimination;<BR>\n" );
document.write( "Multiply the 1st equation by 83 and the 2nd equation by 2:<BR>\n" );
document.write( "166x + 332y = 1411<BR>\n" );
document.write( "166x - 126y = -86<BR>\n" );
document.write( "--------------------subtraction eliminates x, find y<BR>\n" );
document.write( "458y = 1497<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1497%2F458 ALIGN=MIDDLE  ALT=\"1497%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" >; approx 3.3 on the graph<BR>\n" );
document.write( "Find x using eq: 2x + 4y = 17 <BR>\n" );
document.write( "2x + 4(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1497%2F458 ALIGN=MIDDLE  ALT=\"1497%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = 17<BR>\n" );
document.write( "2x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5988%2F458 ALIGN=MIDDLE  ALT=\"5988%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 17<BR>\n" );
document.write( "2x = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5988%2F458 ALIGN=MIDDLE  ALT=\"5988%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 17<BR>\n" );
document.write( "2x = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5988%2F458 ALIGN=MIDDLE  ALT=\"5988%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7786%2F458 ALIGN=MIDDLE  ALT=\"7786%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1798%2F458 ALIGN=MIDDLE  ALT=\"1798%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1798%2F458 ALIGN=MIDDLE  ALT=\"1798%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1798%2F916 ALIGN=MIDDLE  ALT=\"1798%2F916\"   DISABLED_style= \"max-width:90%; height:auto;\" >; approx 2.0 on the graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "solution: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1798%2F458 ALIGN=MIDDLE  ALT=\"1798%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" >; y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1497%2F458 ALIGN=MIDDLE  ALT=\"1497%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" >; this the point of intersection<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Put both equations in the slope intercept form <BR>\n" );
document.write( "2x + 4y = 17<BR>\n" );
document.write( "4y = -2x + 17<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F4 ALIGN=MIDDLE  ALT=\"-2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F4 ALIGN=MIDDLE  ALT=\"17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F4 ALIGN=MIDDLE  ALT=\"17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot two points<BR>\n" );
document.write( "x = 4; y = 2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (substituted 4 for x in the above equation and found y)<BR>\n" );
document.write( "x = 0; y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F4 ALIGN=MIDDLE  ALT=\"17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; (4.25) this is also the y intercept (when x=0)<BR>\n" );
document.write( "Graph of this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+12%2C+-8%2C+10%2C+-.5x%2B%2817%2F4%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+12%2C+-8%2C+10%2C+-.5x%2B%2817%2F4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "calculate the x intercept (when y = 0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F4 ALIGN=MIDDLE  ALT=\"17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F4 ALIGN=MIDDLE  ALT=\"17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both side by -2, results<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34%2F4 ALIGN=MIDDLE  ALT=\"34%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the x intercept, confirmed on the graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Do the same with the 2nd equation;<BR>\n" );
document.write( "83x - 63y = -43<BR>\n" );
document.write( "-63y = -83x - 43<BR>\n" );
document.write( "63y = 83x + 43; multiplied by -1<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83%2F63 ALIGN=MIDDLE  ALT=\"83%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43%2F63 ALIGN=MIDDLE  ALT=\"43%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot two points<BR>\n" );
document.write( "x = 0, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43%2F63 ALIGN=MIDDLE  ALT=\"43%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" >; approx .7 on the graph; this the y intercept<BR>\n" );
document.write( "x = 4, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=375%2F63 ALIGN=MIDDLE  ALT=\"375%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" >; approx 6 on the graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Add this to the above graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+12%2C+-8%2C+10%2C+-.5x%2B%2817%2F4%29%2C+%2883%2F63%29x%2B%2843%2F63%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Calculate the x intercept of this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83%2F63 ALIGN=MIDDLE  ALT=\"83%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43%2F63 ALIGN=MIDDLE  ALT=\"43%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83%2F63 ALIGN=MIDDLE  ALT=\"83%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43%2F63 ALIGN=MIDDLE  ALT=\"43%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by 63<BR>\n" );
document.write( "83x = 43<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-43%2F83 ALIGN=MIDDLE  ALT=\"-43%2F83\"   DISABLED_style= \"max-width:90%; height:auto;\" >; approx -.5 on the graph, (the x intercept\r<BR>\n" );
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document.write( "Summarize<BR>\n" );
document.write( "Eq1: x intercept = 8.5, y intercept = 4.25<BR>\n" );
document.write( "Eq2: x intercept = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-43%2F83 ALIGN=MIDDLE  ALT=\"-43%2F83\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y intercept = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43%2F63 ALIGN=MIDDLE  ALT=\"43%2F63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Point of intersection: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1798%2F458 ALIGN=MIDDLE  ALT=\"1798%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" >; y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1497%2F458 ALIGN=MIDDLE  ALT=\"1497%2F458\"   DISABLED_style= \"max-width:90%; height:auto;\" > (approx 2, 3.3 on the graph<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "This problems was very time consuming, please take time to study it and learn<BR>\n" );
document.write( "what's happening here.  Carl </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );