document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157882>Question 157882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two angles are supplementary of each other. Twice one angle is equal to the other angle minus the product of six and eight. <BR>\n" );
document.write( "	<BR>\n" );
document.write( "Set up a system of linear equations to represent the two angles. Graph each of the equations on one rectangular coordinate system. (Hint: You must get y by itself before graphing.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116335 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two angles are supplementary of each other. Twice one angle is equal to the other angle minus the product of six and eight. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Supplementary angles mean that the sum of two angles equals 180 degrees.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let x = one angle<BR>\n" );
document.write( "and y = the other angle<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since we have two unknowns we'll need two equations.<BR>\n" );
document.write( "From:\"Two angles are supplementary of each other.\" we get:<BR>\n" );
document.write( "x+y = 180<BR>\n" );
document.write( ".<BR>\n" );
document.write( "From:\"Twice one angle is equal to the other angle minus the product of six and eight.\" we get:<BR>\n" );
document.write( "2x = y - (6*8)<BR>\n" );
document.write( "2x = y - 48<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Our \"system of equations\" then is:<BR>\n" );
document.write( "x+y = 180<BR>\n" );
document.write( "2x = y - 48<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the \"hint\" let's get y one side of the equation:<BR>\n" );
document.write( "for<BR>\n" );
document.write( "x+y = 180<BR>\n" );
document.write( "y = -x + 180<BR>\n" );
document.write( "for<BR>\n" );
document.write( "2x = y - 48<BR>\n" );
document.write( "2x + 48 = y<BR>\n" );
document.write( "y = 2x + 48<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now, our system of equations are:<BR>\n" );
document.write( "y = -x + 180<BR>\n" );
document.write( "y = 2x + 48<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Both are now in the \"slope-intercept\" form of<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "where<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept at (0,b)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The idea is the plot each line on a single graph -- where they intersect is where your answer is.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "I'll solve it algebraically here:<BR>\n" );
document.write( "since we have:<BR>\n" );
document.write( "y = -x + 180<BR>\n" );
document.write( "y = 2x + 48<BR>\n" );
document.write( ".<BR>\n" );
document.write( "we can substitute the first into the second to get:<BR>\n" );
document.write( "-x + 180 = 2x + 48<BR>\n" );
document.write( "180 = 3x + 48<BR>\n" );
document.write( "132 = 3x<BR>\n" );
document.write( "44 deg = x (one angle)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solving for the other:<BR>\n" );
document.write( "x+y = 180<BR>\n" );
document.write( "44+y = 180<BR>\n" );
document.write( "y = 180 - 44<BR>\n" );
document.write( "y = 136 deg (other angle) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );