document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184483>Question 184483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	For the systems of linear equations in questions 1-3<BR>\n" );
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 <BR>\n" );
document.write( " 2x + 3y = 8  and  3x + 2y = 7\r<BR>\n" );
document.write( "\n" );
document.write( "help is much appreciated!<BR>\n" );
document.write( "G </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138473 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equations are 1st degree. That means there <BR>\n" );
document.write( "are no powers higher than 1. Two 1st degree<BR>\n" );
document.write( "equations can either:<BR>\n" );
document.write( "(a) Be 2 parallel straight lines<BR>\n" );
document.write( "(b) Be 2 straight lines that intersect at 1 point<BR>\n" );
document.write( "(c) Be the same equation written twice<BR>\n" );
document.write( "If there're parallel, they're lines with the <BR>\n" );
document.write( "same slope, and have no solution. If they're<BR>\n" );
document.write( "not parallel, they must have a solution<BR>\n" );
document.write( "I'll put them in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" >= slope. If the slope is the same, there's<BR>\n" );
document.write( "no solution<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+3y+=+8 ALIGN=MIDDLE  ALT=\"+2x+%2B+3y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+2y+=+7 ALIGN=MIDDLE  ALT=\"+3x+%2B+2y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+3y+=+8 ALIGN=MIDDLE  ALT=\"+2x+%2B+3y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+-2x+%2B+8 ALIGN=MIDDLE  ALT=\"3y+=+-2x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%282%2F3%29x+%2B+%288%2F3%29 ALIGN=MIDDLE  ALT=\"y+=+-%282%2F3%29x+%2B+%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+2y+=+7 ALIGN=MIDDLE  ALT=\"+3x+%2B+2y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+-3x+%2B+7 ALIGN=MIDDLE  ALT=\"2y+=+-3x+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%2F2%29x+%2B+%287%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+-%283%2F2%29x+%2B+%287%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "The slopes are not the same, so there is a solution<BR>\n" );
document.write( "To solve, I'll multiply (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+%2B+6y+=+16 ALIGN=MIDDLE  ALT=\"+4x+%2B+6y+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x+%2B+6y+=+21 ALIGN=MIDDLE  ALT=\"+9x+%2B+6y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now subtract (1) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x+%2B+6y+=+21 ALIGN=MIDDLE  ALT=\"+9x+%2B+6y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x+-+6y+=+-16 ALIGN=MIDDLE  ALT=\"+-4x+-+6y+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+5 ALIGN=MIDDLE  ALT=\"5x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Put this back into either equation to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2A1+%2B+6y+=+16 ALIGN=MIDDLE  ALT=\"+4%2A1+%2B+6y+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y+=+16+-+4 ALIGN=MIDDLE  ALT=\"6y+=+16+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2 ALIGN=MIDDLE  ALT=\"y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This tells me that the point of intersection is (1,2)<BR>\n" );
document.write( "Now I'll plot them<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+-%282%2F3%29x+%2B+8%2F3%2C-%283%2F2%29x+%2B+7%2F2+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For each line, to find the x-intercept, set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for the y-intercept </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );