document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56846>Question 56846</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0028251784/algebrahomeworkh>Glencoe Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of the vertices of the triangle whose sides are contained in the lines whose equations are 5x - 3y = -7, x + 2y = 9, and 3x - 7y = 1.\r<BR>\n" );
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document.write( "5x - 3y = -7<BR>\n" );
document.write( " x + 2y = 9 --> x = -2y + 9<BR>\n" );
document.write( "3x - 7y = 1\r<BR>\n" );
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document.write( "5(-2y + 9) - 3y = -7<BR>\n" );
document.write( "-10y + 45 - 3y = -7<BR>\n" );
document.write( "-13y + 45 = -7<BR>\n" );
document.write( "     - 45 on both sides<BR>\n" );
document.write( "-13y = -52<BR>\n" );
document.write( "    divide by -13 on both sides<BR>\n" );
document.write( "y = 4\r<BR>\n" );
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document.write( "put 4 back into the equation to find x:<BR>\n" );
document.write( "5x - 3(4) = -7<BR>\n" );
document.write( "5x - 12 = -7<BR>\n" );
document.write( "    add 12 to both sides:<BR>\n" );
document.write( "5x = 5<BR>\n" );
document.write( "x = 1\r<BR>\n" );
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document.write( "(1, 4)\r<BR>\n" );
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document.write( "check answers:<BR>\n" );
document.write( "5x - 3y = -7 --> 5(1) - 3(4) = 5 - 12 = -7  (correct)<BR>\n" );
document.write( " x + 2y = 9  --> 1 + 2(4) = 1 + 8 = 9  (correct)<BR>\n" );
document.write( "3x - 7y = 1  --> 3(1) - 7(4) = 3 - 28 = -25 is not equal to 1.  (incorrect) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38686 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=38686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of the vertices of the triangle whose sides are contained in the lines whose equations are 5x - 3y = -7, x + 2y = 9, and 3x - 7y = 1.\r<BR>\n" );
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document.write( "5x - 3y = -7<BR>\n" );
document.write( " x + 2y = 9 --> x = -2y + 9<BR>\n" );
document.write( "3x - 7y = 1\r<BR>\n" );
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document.write( "5(-2y + 9) - 3y = -7<BR>\n" );
document.write( "-10y + 45 - 3y = -7<BR>\n" );
document.write( "-13y + 45 = -7<BR>\n" );
document.write( "     - 45 on both sides<BR>\n" );
document.write( "-13y = -52<BR>\n" );
document.write( "    divide by -13 on both sides<BR>\n" );
document.write( "y = 4\r<BR>\n" );
document.write( "\n" );
document.write( "put 4 back into the equation to find x:<BR>\n" );
document.write( "5x - 3(4) = -7<BR>\n" );
document.write( "5x - 12 = -7<BR>\n" );
document.write( "    add 12 to both sides:<BR>\n" );
document.write( "5x = 5<BR>\n" );
document.write( "x = 1\r<BR>\n" );
document.write( "\n" );
document.write( "(1, 4)\r<BR>\n" );
document.write( "\n" );
document.write( "check answers:<BR>\n" );
document.write( "5x - 3y = -7 --> 5(1) - 3(4) = 5 - 12 = -7  (correct)<BR>\n" );
document.write( " x + 2y = 9  --> 1 + 2(4) = 1 + 8 = 9  (correct)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You were right about the first vertex, but there are three vertices in a triangle.  <BR>\n" );
document.write( "Look at the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-5x-7%29%2F-3%2C%28-x%2B9%29%2F2%2C%28-3x%2B1%29%2F-7%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The red line is: 5x-3y=-7<BR>\n" );
document.write( "The green line is: x+2y=9<BR>\n" );
document.write( "The blue line is: 3x-7y=1<BR>\n" );
document.write( "You found 1, the intersection of:<BR>\n" );
document.write( "5x-3y=-7 and x+2y=9<BR>\n" );
document.write( "Now you have to find the intersection of:<BR>\n" );
document.write( "5x-3y=-7 and 3x-7y=1<BR>\n" );
document.write( "Since you know how to do that, I'll just give you and answer to check yourself against.  If you don't get that answer, let me know and I'll elaberate: (-2,-1)<BR>\n" );
document.write( "Finally you have to find the intersection of:<BR>\n" );
document.write( "x+2y=9 and 3x-7y=1  Check your answer against: (5,2).<BR>\n" );
document.write( "Let me know, if you need more information.  I think you are on the right track and just needed a nudge.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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