document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142955>Question 1142955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the simultaneous equation:<BR>\n" );
document.write( "4x² - 9y² = 19<BR>\n" );
document.write( "2x + 3y = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763717 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The line 2x +3y = 1 is tangent to 4x^2 -9y^2 = 19<BR>\n" );
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document.write( "Solve the linear equation for y<BR>\n" );
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document.write( "1) y = -2x/3 +1/3<BR>\n" );
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document.write( "substitute for y in the equation of the hyperbole<BR>\n" );
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document.write( "4x^2 -9(-2x/3 +1/3)^2 = 19<BR>\n" );
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document.write( "4x^2 -9(4x^2/9 -4x/9 +1/9) = 19<BR>\n" );
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document.write( "4x^2 -4x^2 +4x -1 = 19<BR>\n" );
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document.write( "4x -20 = 0<BR>\n" );
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document.write( "4x = 20<BR>\n" );
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document.write( "x = 5<BR>\n" );
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document.write( "use equation 1 to get the value of y<BR>\n" );
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document.write( "y = -2(5)/3 +1/3 = -3<BR>\n" );
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document.write( "solution is x = 5, y = -3 which is the point (5, -3)<BR>\n" );
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document.write( "check the solution<BR>\n" );
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document.write( "hyperbole <BR>\n" );
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document.write( "4(5^2) -9(-3)^2 = 19<BR>\n" );
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document.write( "100 -81 = 19<BR>\n" );
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document.write( "19 = 19<BR>\n" );
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document.write( "Line<BR>\n" );
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document.write( "2(5) +3(-3) = 1<BR>\n" );
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document.write( "10 -9 = 1<BR>\n" );
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document.write( "1 = 1<BR>\n" );
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document.write( "answers check<BR>\n" );
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