document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=816184>Question 816184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My son just does not understand this from the teacher's explanation.  If you would please break down the steps to solve this one problem, hopefully we can apply the principals to the other problems.   Thank you very much.\r<BR>\n" );
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document.write( "        2x + 3y = -1\r<BR>\n" );
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document.write( "        3x + 4y = -4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491413 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=491413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x + 3y = -1 <BR>\n" );
document.write( "3x + 4y = -4<BR>\n" );
document.write( "This problem can be solved two ways<BR>\n" );
document.write( "1)  substitution<BR>\n" );
document.write( "solve first equation for x<BR>\n" );
document.write( "2x = -1 -3y<BR>\n" );
document.write( "x = (-1 -3y) / 2<BR>\n" );
document.write( "substitute for x in second equation<BR>\n" );
document.write( "3*(-1 -3y)/2 +4y = -4<BR>\n" );
document.write( "multiply both sides of = by 2<BR>\n" );
document.write( "3*(-1 -3y) +8y = -8<BR>\n" );
document.write( "-3 -9y +8y = -8<BR>\n" );
document.write( "-y = -5<BR>\n" );
document.write( "y = 5 <BR>\n" );
document.write( "solve for x in first equation<BR>\n" );
document.write( "2x +3*(5) = -1<BR>\n" );
document.write( "2x = -16<BR>\n" );
document.write( "x = -8<BR>\n" );
document.write( "check answers in second equation<BR>\n" );
document.write( "3*-8 +4*5 = -4<BR>\n" );
document.write( "-24 +20 = -4<BR>\n" );
document.write( "-4 = -4<BR>\n" );
document.write( "therefore <BR>\n" );
document.write( "x = -8 and y = 5 is the correct solution<BR>\n" );
document.write( "2) solve system of linear equations using matrices<BR>\n" );
document.write( "2x + 3y = -1 <BR>\n" );
document.write( "3x + 4y = -4<BR>\n" );
document.write( "first write the augmented matrix using the coefficients with the right column contains the constants<BR>\n" );
document.write( "| 2  3  | -1 |<BR>\n" );
document.write( "| 3  4  | -4 |<BR>\n" );
document.write( "The objective is to reorganize the original matrix into one that looks like<BR>\n" );
document.write( "| 1  0  |  a |<BR>\n" );
document.write( "| 0  1  |  b |<BR>\n" );
document.write( "where a and b are the solutions to the system<BR>\n" );
document.write( "multiply row 2 by -1 and add to row 1<BR>\n" );
document.write( "| -1 -1  |  3 |<BR>\n" );
document.write( "|  3  4  | -4 |<BR>\n" );
document.write( "multiply row 1 by 3 and add to row 2<BR>\n" );
document.write( "| -1 -1  |  3 |<BR>\n" );
document.write( "|  0  1  |  5 |<BR>\n" );
document.write( "add row 2 to row 1<BR>\n" );
document.write( "| -1  0  |  8 |<BR>\n" );
document.write( "|  0  1  |  5 |<BR>\n" );
document.write( "multiply row 1 by -1<BR>\n" );
document.write( "|  1  0  | -8 |<BR>\n" );
document.write( "|  0  1  |  5 |<BR>\n" );
document.write( "This gives us the solution x = -8 and y = 5<BR>\n" );
document.write( "Note that this matches with our substitution solution in 1)   :-)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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