document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114564>Question 114564</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321168305/algebrahomeworkh>Algebra for College Students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I just need to solve the matrix-I do know the answer, however, I'm not sure of how to do the problem.\r<BR>\n" );
document.write( "\n" );
document.write( "3x+4y=13<BR>\n" );
document.write( "2x-3y=-14\r<BR>\n" );
document.write( "\n" );
document.write( "the answer is (-1,4)\r<BR>\n" );
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document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83348 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x+4y=13<BR>\n" );
document.write( "2x-3y=-14<BR>\n" );
document.write( "In matrix form, it would look like,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3%0D%0A+%29%0D%0A%29%28+matrix%28+2%2C+1%2C+%0D%0A+++x%2C+y+%29%29=%28+matrix%28+2%2C+1%2C+%0D%0A+++13%2C+-14+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >][<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >]=[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >] <BR>\n" );
document.write( "The solution is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A+matrix%28+2%2C+1%2C+%0D%0A+++x%2C+y%0D%0A+%29%29=%28+%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++k%2C+l%2C%0D%0A+++m%2C+n+%0D%0A%29%29%28+%0D%0A+matrix%28+2%2C+1%2C+%0D%0A+++13%2C+-14+%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where k,l,m,n are coefficients of the inverse matrix of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE  ALT=\"%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3%0D%0A+%29%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >]=[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E-1 ALIGN=MIDDLE  ALT=\"A%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >][<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >] <BR>\n" );
document.write( "The inverse of a 2x2 matrix, A, where   <BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++a%2C+b%2C%0D%0A+++c%2C+d%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE  ALT=\"%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++a%2C+b%2C%0D%0A+++c%2C+d%0D%0A+%29%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is given by<BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E-1 ALIGN=MIDDLE  ALT=\"A%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >]= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28ad-bc%29%29%2A%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++d%2C+-b%2C%0D%0A+++-c%2C+a%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using your coefficients in the inverse matrix formula,<BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E-1 ALIGN=MIDDLE  ALT=\"A%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >]=  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%283%28-3%29-4%282%29%29%29%2A%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E-1 ALIGN=MIDDLE  ALT=\"A%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >]=   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F17%29%2A%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++-3%2C+-4%2C%0D%0A+++-2%2C+3%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E-1 ALIGN=MIDDLE  ALT=\"A%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >]=   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F17%29%2A%28%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution is therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A+matrix%28+2%2C+1%2C+%0D%0A+++x%2C+y%0D%0A+%29%29=%281%2F17%29%2A%28+%0D%0A+matrix%28+2%2C+2%2C+%0D%0A+++3%2C+4%2C%0D%0A+++2%2C+-3+%0D%0A%29%29%28+%0D%0A+matrix%28+2%2C+1%2C+%0D%0A+++13%2C+-14+%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's carry out each calculation separately, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F17%29%2A%283%2813%29%2B%284%29%28-14%29%29 ALIGN=MIDDLE  ALT=\"x=%281%2F17%29%2A%283%2813%29%2B%284%29%28-14%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F17%29%2A%2839-56%29 ALIGN=MIDDLE  ALT=\"x=%281%2F17%29%2A%2839-56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F17%29%2A%28-17%29 ALIGN=MIDDLE  ALT=\"x=%281%2F17%29%2A%28-17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F17%29%2A%282%2813%29%2B%28-3%29%28-14%29%29 ALIGN=MIDDLE  ALT=\"y=%281%2F17%29%2A%282%2813%29%2B%28-3%29%28-14%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F17%29%2A%2826%2B42%29 ALIGN=MIDDLE  ALT=\"y=%281%2F17%29%2A%2826%2B42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F17%29%2A%2868%29 ALIGN=MIDDLE  ALT=\"y=%281%2F17%29%2A%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A+matrix%28+2%2C+1%2C+%0D%0A+++x%2C+y%0D%0A+%29%29=%28%0D%0A+matrix%28+2%2C+1%2C+%0D%0A+++-1%2C+4%0D%0A+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );