document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163044>Question 163044</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>saxon algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Graph and describe the shape that the lines form.\r<BR>\n" );
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document.write( "3x-2y=2<BR>\n" );
document.write( "-3x-2y=-34<BR>\n" );
document.write( "x-2y=6\r<BR>\n" );
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document.write( "find the vertices of the shape. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124393 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph and describe the shape that the lines form. <BR>\n" );
document.write( "3x-2y=2<BR>\n" );
document.write( "-3x-2y=-34<BR>\n" );
document.write( "x-2y=6 <BR>\n" );
document.write( "find the vertices of the shape.<BR>\n" );
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document.write( "Since they're 3 straight lines, the \"shape they form\", or any space they enclose can only be a triangle.  If 2 of them are parallel, they won't enclose any space.<BR>\n" );
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document.write( "To find the 3 vertices, solve the eqns in pairs, ie, eqn 1&2, eqn 1&3, eqn 2&3.<BR>\n" );
document.write( "1) 3x-2y=2<BR>\n" );
document.write( "2) -3x-2y=-34<BR>\n" );
document.write( "3) x-2y=6 <BR>\n" );
document.write( "Check the slopes of each to see if any are parallel:<BR>\n" );
document.write( "1) m = 3/2<BR>\n" );
document.write( "2) m = -3/2<BR>\n" );
document.write( "3) m = 1/2<BR>\n" );
document.write( "The slopes are different, so no 2 lines are parallel.  Also, no 2 lines are perpendicular, so it's not a right triangle.<BR>\n" );
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document.write( "1 & 2:<BR>\n" );
document.write( "1) 3x-2y=2<BR>\n" );
document.write( "2) -3x-2y=-34<BR>\n" );
document.write( "Add them<BR>\n" );
document.write( "0x -4y = -32<BR>\n" );
document.write( "y = 8<BR>\n" );
document.write( "Sub into 1:<BR>\n" );
document.write( "3x - 2*8 = 2<BR>\n" );
document.write( "3x = 18<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "So the vertex is (6,8)<BR>\n" );
document.write( "1 & 3:<BR>\n" );
document.write( "1) 3x-2y=2<BR>\n" );
document.write( "3) x-2y=6 <BR>\n" );
document.write( "Subtract 3 from 1<BR>\n" );
document.write( "2x = -4<BR>\n" );
document.write( "x = -2<BR>\n" );
document.write( "3) -2 - 2y = 6<BR>\n" );
document.write( "-2y = 8<BR>\n" );
document.write( "y = -4<BR>\n" );
document.write( "The 2nd vertex is (-2,-4)<BR>\n" );
document.write( "2 & 3:<BR>\n" );
document.write( "2) -3x-2y=-34<BR>\n" );
document.write( "3) x-2y=6 <BR>\n" );
document.write( "Subtract 3 from 2<BR>\n" );
document.write( "-4x = -40<BR>\n" );
document.write( "x = 10<BR>\n" );
document.write( "Sub into 3<BR>\n" );
document.write( "10 - 2y = 6<BR>\n" );
document.write( "-2y = -4<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "Vertex #3 is (10,2)<BR>\n" );
document.write( "So it is a triangle with vertices at (10,2), (-2,-4) and (6,8)<BR>\n" );
document.write( "The lengths of the sides and the angles can be found, but it wasn't asked for.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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