document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374881>Question 374881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am really struggling in math right now. I am working on word problems for linear systems, and Unfortunately I don't have a clue what to do, so i need some answers from you, to look them over and examine them to get a clue of what i'm trying to do.\r<BR>\n" );
document.write( "\n" );
document.write( "1. Find the equation of the line that passes through the point of intersection of -2x + 4y = 14 and 5x - 3y = -14 and is perpendicular to 2x - 3y + 6 = 0.\r<BR>\n" );
document.write( "\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 #266799 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=266799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Find the equation of the line that passes through the point of intersection of -2x + 4y = 14 and 5x - 3y = -14 and is perpendicular to 2x - 3y + 6 = 0. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "First of all find the point of intersection by solving the system, x & y<BR>\n" );
document.write( "-2x + 4y = 14<BR>\n" );
document.write( "+5x - 3y = -14<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 5, the 2nd equation by 2, results:<BR>\n" );
document.write( "-10x + 20y = 70<BR>\n" );
document.write( "+10x - 6y = -28<BR>\n" );
document.write( "------------------adding eliminates x, find y<BR>\n" );
document.write( "14y = 42<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F14 ALIGN=MIDDLE  ALT=\"42%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find x using the 2nd equation: +5x - 3y = -14; replace y with 3<BR>\n" );
document.write( "5x - 3(3) = -14<BR>\n" );
document.write( "5x - 9 = -14<BR>\n" );
document.write( "5x = -14 + 9<BR>\n" );
document.write( "5x = -5<BR>\n" );
document.write( "x = -1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The point of intersection: x=-1, y=3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We want the equation of a line that is perpendicular to 2x - 3y + 6 = 0<BR>\n" );
document.write( "and pass thru the point x=-1, y=3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the slope of the equation 2x - 3y + 6 = 0, put it in the slope/intercept form, namely: y = mx + b<BR>\n" );
document.write( "2x - 3y + 6 = 0<BR>\n" );
document.write( "subtract 2x and 6 from both sides<BR>\n" );
document.write( "-3y = -2x - 6<BR>\n" );
document.write( "Y has to be positive, mult by -1<BR>\n" );
document.write( "3y = 2x + 6<BR>\n" );
document.write( "Divide both sides by 3<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 2<BR>\n" );
document.write( "The slope: m1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "The relationship of the slopes of perpendicular lines is m1*m2 = -1<BR>\n" );
document.write( "we know m1, find m2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >*m2 = -1<BR>\n" );
document.write( "divide both sides by 3/2<BR>\n" );
document.write( "m2 = -1*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the point/slope form: y - y1 = m(x - x1)<BR>\n" );
document.write( "x1=-1; y1=3 (the point of intersection)<BR>\n" );
document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so we have:<BR>\n" );
document.write( "y - 3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >[x - (-1)]<BR>\n" );
document.write( "y - 3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >[x + 1]<BR>\n" );
document.write( "y - 3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 3 to both sides<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3<BR>\n" );
document.write( "which is<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2 ALIGN=MIDDLE  ALT=\"6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Put in the standard form, multiply by 2<BR>\n" );
document.write( "2y = -3x + 3<BR>\n" );
document.write( "Add 3x to both sides<BR>\n" );
document.write( "3x + 2y = 3; is the equation of a line that passes  thru the intersecting point -1,3<BR>\n" );
document.write( "and is perpendicular to the line 2x - 3y + 6 = 0. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );