document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146738>Question 146738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve this Using augmented matrices to solve the following 2 x 2 systems of equations. Show all work.\r<BR>\n" );
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document.write( "1.  3x + 4y = 11<BR>\n" );
document.write( "     x + 3y  = 2\r<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 #107168 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you started with:<BR>\n" );
document.write( "  3x + 4y = 11<BR>\n" );
document.write( "   x + 3y  = 2<BR>\n" );
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document.write( "The \"coefficient matrix\" is:<BR>\n" );
document.write( "3 4<BR>\n" );
document.write( "1 3<BR>\n" );
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document.write( "The determinant of the \"coefficient matrix\" is:<BR>\n" );
document.write( "(3*3) - (1*4) = 9 -4 = 5<BR>\n" );
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document.write( "The 'x' matrix is:<BR>\n" );
document.write( "11 4<BR>\n" );
document.write( " 2 3<BR>\n" );
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document.write( "The determinant of the 'x' matrix is:<BR>\n" );
document.write( "(11*3)-(2*4) = 33 -8 = 25<BR>\n" );
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document.write( "The 'y' matrix is:<BR>\n" );
document.write( "3 11<BR>\n" );
document.write( "1  2<BR>\n" );
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document.write( "The determinant of the 'y' matrix is:<BR>\n" );
document.write( "(2*3)-(1*11) = 6 -11 = -5<BR>\n" );
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document.write( "Solution for 'x' is \"det of x\"/\"det of coefficient\":<BR>\n" );
document.write( "25/5 = 5 <BR>\n" );
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document.write( "Solution for 'y' is \"det of y\"/\"det of coefficient\":<BR>\n" );
document.write( "-5/5 = -1<BR>\n" );
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document.write( "Our solution is (x,y) = (5,-1)<BR>\n" );
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document.write( "To check, plug it back into:<BR>\n" );
document.write( "   x + 3y  = 2<BR>\n" );
document.write( "   5 + 3(-1)  = 2<BR>\n" );
document.write( "   5 - 3  = 2<BR>\n" );
document.write( "       2 = 2 (check)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "  3x + 4y = 11<BR>\n" );
document.write( "  3(5) + 4(-1) = 11<BR>\n" );
document.write( "  15 - 4 = 11<BR>\n" );
document.write( "       11 = 11 (check)\r<BR>\n" );
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