document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935881>Question 935881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the straight line L1: 3x+y-9=0 and L2: 2x-9y+k=o have the same x-intercept, find <BR>\n" );
document.write( "(a) the value of k <BR>\n" );
document.write( "(b) the y-intercept </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569246 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=569246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first equation is 3x + y - 9 = 0<BR>\n" );
document.write( "second equation is 2x + 9y - k = 0\r<BR>\n" );
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document.write( "solve for y in both equations.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "first equation becomes y = -3x + 9<BR>\n" );
document.write( "second equation becomes y = (-2x+k)/9\r<BR>\n" );
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document.write( "the x-intercept occurs when the value of y is equal to 0.\r<BR>\n" );
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document.write( "set both equations equal to 0 to get:\r<BR>\n" );
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document.write( "first equation becomes -3x + 9 = 0<BR>\n" );
document.write( "second equation becomes (-2x+i)/9 = 0\r<BR>\n" );
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document.write( "solve for x in the first equation to get x = 3<BR>\n" );
document.write( "solve for x in the second equation to get 2x = k\r<BR>\n" );
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document.write( "when y = 0, the value of x in both equations must be the same since both equations have the same x-intercept, so the second equation becomes 2(3) = k.\r<BR>\n" );
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document.write( "solve for k in the second equation to get k = 6.\r<BR>\n" );
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document.write( "both equations will have the same x-intercept when k = 6.\r<BR>\n" );
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document.write( "when k = 6, the second equation becomes y = (-2x + 6) / 9\r<BR>\n" );
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document.write( "the equations are now:\r<BR>\n" );
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document.write( "first equation is y = -3x + 9<BR>\n" );
document.write( "second equation is y = (-2x + 6)/9\r<BR>\n" );
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document.write( "the y-intercept is the value of y when x is equal to 0.\r<BR>\n" );
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document.write( "replace x with 0 in both equations to get:\r<BR>\n" );
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document.write( "first equation becomes y = 9<BR>\n" );
document.write( "second equation becomes y = 2/3.\r<BR>\n" );
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document.write( "the y-intercept for the first equation is 9.<BR>\n" );
document.write( "the y intercept for the second equation is y = 2/3.\r<BR>\n" );
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document.write( "the graph of both equations is shown below:\r<BR>\n" );
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document.write( "i placed 2 horizontal lines at y = 9 and y = 2/3, so you can see the y-intercepts better.\r<BR>\n" );
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document.write( "the line that crosses the y-axis at y = 2/3 is the second equation.<BR>\n" );
document.write( "the line that crosses the y-axis at y = 9 is the first equation.\r<BR>\n" );
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document.write( "the equation of the lowest horizontal line is y = 2/3.<BR>\n" );
document.write( "the equation of the highest horizontal line is y = 9.\r<BR>\n" );
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