document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014326>Question 1014326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The three lines y=x-1, y=4-2x, y=-x-5 intersect to form a triangle. Determine the coordinates of the vertices of the triangle.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630628 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=630628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to solve 3 sets of 2 equations that need to be solved simultaneously.<BR>\n" );
document.write( "this will get you the 3 intersection points.\r<BR>\n" );
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document.write( "first set is y = x-1 and y = 4-2x<BR>\n" );
document.write( "second set is y = x-1 and y = -x-5<BR>\n" );
document.write( "third set is y = 4-2x and y = -x-5\r<BR>\n" );
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document.write( "first set:<BR>\n" );
document.write( "start with y = x-1 and y = 4-2x<BR>\n" );
document.write( "since both x-1 and 4-2x are equal to y, you can set them equal to each other and solve for x.<BR>\n" );
document.write( "start with x-1 = 4-2x<BR>\n" );
document.write( "add 2x to both sides of the euation and add 1 to both sides of the equation to get 2x + x = 4 + 1<BR>\n" );
document.write( "combine like terms to get 3x = 5<BR>\n" );
document.write( "divide both sides of the equation by 3 to get x = 5/3 = 1 and 2/3 = 1.666...<BR>\n" );
document.write( "when x = 5/3, y = x-1 gets you y = 5/3 - 1 which gets you y = 2/3.<BR>\n" );
document.write( "you have x = 1.67 and y = .67.<BR>\n" );
document.write( "your intersection point is (1.67,.67) rounded to 2 decimal places.\r<BR>\n" );
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document.write( "second set:<BR>\n" );
document.write( "start with y = x-1 and y = -x-5<BR>\n" );
document.write( "since both x-1 and -x-5 are equal to y, you can set them equal to each other to get x-1 = -x-5<BR>\n" );
document.write( "add x to both sides of the equation and add 1 to both sides of the equation to get x + x = -5 + 1<BR>\n" );
document.write( "combine like terms to get 2x = -4<BR>\n" );
document.write( "divide both sides by 2 to get x = -2<BR>\n" );
document.write( "when x = -2, y = x-1 gets you y = -2-1 which gets you y = -3<BR>\n" );
document.write( "you have x = -2 and y = -3.<BR>\n" );
document.write( "your intersection point is (-2,-3)\r<BR>\n" );
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document.write( "third set:<BR>\n" );
document.write( "start with y = 4-2x and y = -x-5.<BR>\n" );
document.write( "since both 4-2x and -x-5 are equal to 6, you can set them equal to each other to get 4-2x = -x-5.<BR>\n" );
document.write( "add x to both sides of the equation and subtract 4 from both sides of the equation to get -2x + x = -5 - 4.<BR>\n" );
document.write( "combine like terms to get -x = -9<BR>\n" );
document.write( "multiply both sides of the equation by -1 to get x = 9<BR>\n" );
document.write( "when x = 9, y = 4-2x gets you y = 4-18 which gets you y = -14.<BR>\n" );
document.write( "you hve x = 9 and y = -14.<BR>\n" );
document.write( "your intersection point is (9,-14)\r<BR>\n" );
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document.write( "you have 3 intersection points which form your triangle.<BR>\n" );
document.write( "on the graph, the intersection points are the coordinate points.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "(1.67,.67)<BR>\n" );
document.write( "(-2,-3)<BR>\n" );
document.write( "(9,-14)\r<BR>\n" );
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document.write( "i graphed the three equations and marked the intersection points.<BR>\n" );
document.write( "they agree.<BR>\n" );
document.write( "on the graph 1.67 is shown as 1.667.<BR>\n" );
document.write( "that's the same x-coordinate with different rounding applied.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/011801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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