document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557102>Question 557102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the measurement of angle 1 =2x+40<BR>\n" );
document.write( "the measurement of angle 2 =2y+40<BR>\n" );
document.write( "the measurement of angle 3 =x+2y<BR>\n" );
document.write( "And there is a picture that looks roughly like this:<BR>\n" );
document.write( "('e's are used to provide correct spacing<BR>\n" );
document.write( "eeeee^<BR>\n" );
document.write( "eeeeee\<BR>\n" );
document.write( "eeeeeee\<BR>\n" );
document.write( "eeeeee1e\ee2<BR>\n" );
document.write( "<--------------------><BR>\n" );
document.write( "eeeeeeeeee\ 3<BR>\n" );
document.write( "eeeeeeeeeee\<BR>\n" );
document.write( "eeeeeeeeeeee\<BR>\n" );
document.write( "eeeeeeeeeeeeev </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362452 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=362452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-5%2C0%2C5%2C0%29%2C%0D%0Aline%28-2%2C5%2C2%2C-5%29%2Clocate%28-1%2C1%2C1%29%2C+locate%280%2C1%2C2%29%2Clocate%280.5%2C-.2%2C3%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Angles 1 and 3 are vertical to each other; angle 2 is supplementary to 1 and to 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B40=x%2B2y ALIGN=MIDDLE  ALT=\"2x%2B40=x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (angles 1 and 3 have the same measure)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B40%29%2B%282y%2B40%29=180 ALIGN=MIDDLE  ALT=\"%282x%2B40%29%2B%282y%2B40%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > (measures of angles 1 and 2 add to 180°)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%2B40%29%2B%28x%2B2y%29=180 ALIGN=MIDDLE  ALT=\"%282y%2B40%29%2B%28x%2B2y%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > (measures of angles 2 and 3 add to 180°)<BR>\n" );
document.write( "That gives you 3 equations on 2 variables.<BR>\n" );
document.write( "Let's simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B40=x%2B2y ALIGN=MIDDLE  ALT=\"2x%2B40=x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=-40 ALIGN=MIDDLE  ALT=\"x-2y=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B40%29%2B%282y%2B40%29=180 ALIGN=MIDDLE  ALT=\"%282x%2B40%29%2B%282y%2B40%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y%2B80=180 ALIGN=MIDDLE  ALT=\"2x%2B2y%2B80=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=100 ALIGN=MIDDLE  ALT=\"2x%2B2y=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%2B40%29%2B%28x%2B2y%29=180 ALIGN=MIDDLE  ALT=\"%282y%2B40%29%2B%28x%2B2y%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y%2B40=180 ALIGN=MIDDLE  ALT=\"x%2B4y%2B40=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y=140 ALIGN=MIDDLE  ALT=\"x%2B4y=140\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With two of the equations we may find a solution, which we would need to substitute in the other equation to see that it verifies.<BR>\n" );
document.write( "If we take the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y=140 ALIGN=MIDDLE  ALT=\"x%2B4y=140\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtracting the first equation from the second, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=90 ALIGN=MIDDLE  ALT=\"3y=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=30 ALIGN=MIDDLE  ALT=\"y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and substituting into the first equation we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B30=50 ALIGN=MIDDLE  ALT=\"x%2B30=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=30 ALIGN=MIDDLE  ALT=\"y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=-40 ALIGN=MIDDLE  ALT=\"x-2y=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then (x,y)=(20,30) is the solution. If not, there is no solution.<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=30 ALIGN=MIDDLE  ALT=\"y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=20-2%2A30=20-60=-40 ALIGN=MIDDLE  ALT=\"x-2y=20-2%2A30=20-60=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so (20,30)<BR>\n" );
document.write( "(or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=30 ALIGN=MIDDLE  ALT=\"y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) is the solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );