document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24981>Question 24981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with a problem.We are learning to solve systems by graphing and locating the point of intersection.<BR>\n" );
document.write( "I know how to graph each system....by the slope and y-intercept, but when it comes to drawing the graph, the point of intersection is wrong.  Is there a special way to start graphing the equation - top to bottom or from bottom to top.<BR>\n" );
document.write( "Here are 2 problems: y=3/4x-4  the slope is 3/4<BR>\n" );
document.write( "                               the y-intercept is -4<BR>\n" );
document.write( "                     <BR>\n" );
document.write( "                     y=-1/2x+6  slope is -1/2<BR>\n" );
document.write( "                                y-intercept is 6\r<BR>\n" );
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document.write( " the point of intersection or coordinates I got was (6,1)\r<BR>\n" );
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document.write( "y=-2x+5   slope is -2/1<BR>\n" );
document.write( "          y-intercept is 5\r<BR>\n" );
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document.write( "y=x-10    slope is 1<BR>\n" );
document.write( "          y-intercept is -10<BR>\n" );
document.write( "point of intersection or coordinate i got was (7,-3)\r<BR>\n" );
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document.write( "Can there be different coordinates or only one?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13387 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=13387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the coordinates at the point of intersection must solve both equations <BR>\n" );
document.write( "because the point is ON both equations, so just make sure that is true<BR>\n" );
document.write( "(1) y = 3/4x - 4<BR>\n" );
document.write( "(2) y = (-1/2)x + 6<BR>\n" );
document.write( "subtract  (2) from (1) <BR>\n" );
document.write( "(3) 0 = (3/4x - 4) - ((-1/2)x + 6)<BR>\n" );
document.write( "(4) 0 = (5/4)x - 10<BR>\n" );
document.write( "(5) (5/4)x = 10<BR>\n" );
document.write( "(6) 5x = 40<BR>\n" );
document.write( "(7) x = 8<BR>\n" );
document.write( "now solve for y in either equation<BR>\n" );
document.write( "(8) y = ((3/4)*8) - 4<BR>\n" );
document.write( "(9) y = 6 - 4<BR>\n" );
document.write( "(10) y = 2<BR>\n" );
document.write( "that means the point (8, 2) is on both lines , thus it is the intersection<BR>\n" );
document.write( "check it with the other equation<BR>\n" );
document.write( "(11) 2 = ((-1/2) * 8) + 6<BR>\n" );
document.write( "is this true? <BR>\n" );
document.write( "(12) 2 = -4 + 6<BR>\n" );
document.write( "yes<BR>\n" );
document.write( "just go through this whith the other equations and you'll get the intersections<BR>\n" );
document.write( "remember that TWO lines have to intersect unless they're parallel (same slope)<BR>\n" );
document.write( "THREE lines do not necessarily have to intersect all at the same point, though<BR>\n" );
document.write( "taken in pairs, they will have intersections, though </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );