document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631692>Question 631692</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i rearragne and sketch a graph witht the following equations\r<BR>\n" );
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document.write( "4x-y=5<BR>\n" );
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document.write( "3x-2y=8\r<BR>\n" );
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document.write( "with the steps please thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398157 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Those equations are linear equations.<BR>\n" );
document.write( "Their graphs are straight lines.<BR>\n" );
document.write( "To graph a straight line you only need to locate 2 points.<BR>\n" );
document.write( "Sometimes you do not even need to rearrange the equation to figure out 2 points for the line.<BR>\n" );
document.write( "In this case, I would rearrange.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-y=5 ALIGN=MIDDLE  ALT=\"4x-y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-y%2By-5=5%2By-5 ALIGN=MIDDLE  ALT=\"4x-y%2By-5=5%2By-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5 ALIGN=MIDDLE  ALT=\"y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to both sides of the equal sign)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-y%2By-5=5%2By-5 ALIGN=MIDDLE  ALT=\"4x-y%2By-5=5%2By-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5=y ALIGN=MIDDLE  ALT=\"4x-5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-5 ALIGN=MIDDLE  ALT=\"y=4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need 2 points from that line.<BR>\n" );
document.write( "<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;\" > makes calculations easy and give us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (0,-5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2A2-5 ALIGN=MIDDLE  ALT=\"y=4%2A2-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8-5 ALIGN=MIDDLE  ALT=\"y=8-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (2,3) <BR>\n" );
document.write( "We can plot the points and then connect them with a line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C6%2C-6%2C4%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28circle%280%2C-5%2C0.2%29%29%2C+blue%28circle%282%2C3%2C0.2%29%29%2C%0D%0Ablue%28line%28-1%2C-9%2C3%2C7%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Similarly, for the other line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=8 ALIGN=MIDDLE  ALT=\"3x-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y%2B2y-8=8%2B2y-8 ALIGN=MIDDLE  ALT=\"3x-2y%2B2y-8=8%2B2y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-8=2y ALIGN=MIDDLE  ALT=\"3x-8=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=3x-8 ALIGN=MIDDLE  ALT=\"2y=3x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=3x-8 ALIGN=MIDDLE  ALT=\"2y=3x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2F2=%283x-8%29%2F2 ALIGN=MIDDLE  ALT=\"2y%2F2=%283x-8%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2F2-8%2F2 ALIGN=MIDDLE  ALT=\"y=3x%2F2-8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F2%29x-4 ALIGN=MIDDLE  ALT=\"y=%283%2F2%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the point, we can use<BR>\n" );
document.write( "<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;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (0,-4) , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F2%29%2A2-4 ALIGN=MIDDLE  ALT=\"y=%283%2F2%29%2A2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-4 ALIGN=MIDDLE  ALT=\"y=3-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (2,-1)<BR>\n" );
document.write( "Then we add to the graph the new points and connect them with a second line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C6%2C-6%2C4%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28circle%280%2C-5%2C0.2%29%29%2C+blue%28circle%282%2C3%2C0.2%29%29%2C%0D%0Ablue%28line%28-1%2C-9%2C3%2C7%29%29%2C%0D%0Agreen%28circle%280%2C-4%2C0.2%29%29%2C+green%28circle%282%2C-1%2C0.2%29%29%2C%0D%0Agreen%28line%28-4%2C-10%2C6%2C5%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sometimes from the graph you can solve the system of equations.<BR>\n" );
document.write( "In this case, the solutions have fractions, and you cannot guess them from the graph.<BR>\n" );
document.write( "You need to solve the system algebraically, finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F5=0.4 ALIGN=MIDDLE  ALT=\"x=2%2F5=0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-17%2F5=-3.4 ALIGN=MIDDLE  ALT=\"y=-17%2F5=-3.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , to find out that the lines intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17%2F5 ALIGN=MIDDLE  ALT=\"-17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) . </SPAN>\n" );
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