document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193741>Question 1193741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of the variables in the matrices:\r<BR>\n" );
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document.write( "-3 * 2   x       + 2  -1     = -4   z<BR>\n" );
document.write( "     3x  4y        4  -3        22  14\r<BR>\n" );
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document.write( "I couldn't put the bracket around each matrice. The 3 is multiplied by the first matrix.\r<BR>\n" );
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document.write( "Thanks\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 #825774 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The -3 out front the first matrix tells us to multiply -3 by everything inside just that particular matrix.<BR>\n" );
document.write( "This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A-3%2A%28matrix%282%2C2%2C2%2Cx%2C3x%2C4y%29%29%0D%0A=+%0D%0A%28matrix%282%2C2%2C-6%2C-3x%2C-9x%2C-12y%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eg: The 2 turns into -3(2) = -6 in the upper left corner.\r<BR>\n" );
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document.write( "So we go from this given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A-3%2A%28matrix%282%2C2%2C2%2Cx%2C3x%2C4y%29%29%0D%0A%2B%28matrix%282%2C2%2C2%2C-1%2C4%2C-3%29%29%0D%0A=%28matrix%282%2C2%2C-4%2Cz%2C22%2C14%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%282%2C2%2C-6%2C-3x%2C-9x%2C-12y%29%29%0D%0A%2B%28matrix%282%2C2%2C2%2C-1%2C4%2C-3%29%29%0D%0A=%28matrix%282%2C2%2C-4%2Cz%2C22%2C14%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For now, focus on the lower left corner of each given matrix.<BR>\n" );
document.write( "Those bottom left corner entries are: <BR>\n" );
document.write( "-9x, 4, and 22\r<BR>\n" );
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document.write( "The first two lower left corner entries add up to the third entry. Meaning we have the equation -9x+4 = 22<BR>\n" );
document.write( "Effectively, each corner is treated separately to form a different equation. <BR>\n" );
document.write( "Or you can think of it like this template here<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29%0D%0A%2B%28matrix%282%2C2%2Ce%2Cf%2Cg%2Ch%29%29%0D%0A=%28matrix%282%2C2%2Ci%2Cj%2Ck%2Cl%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the lower left corner would yield c+g = k\r<BR>\n" );
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document.write( "Solve for x:<BR>\n" );
document.write( "-9x+4 = 22<BR>\n" );
document.write( "-9x = 22-4<BR>\n" );
document.write( "-9x = 18<BR>\n" );
document.write( "x = 18/(-9)<BR>\n" );
document.write( "x = -2\r<BR>\n" );
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document.write( "Now apply substitution to go from this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%282%2C2%2C-6%2C-3x%2C-9x%2C-12y%29%29%0D%0A%2B%28matrix%282%2C2%2C2%2C-1%2C4%2C-3%29%29%0D%0A=%28matrix%282%2C2%2C-4%2Cz%2C22%2C14%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%282%2C2%2C-6%2C6%2C18%2C-12y%29%29%0D%0A%2B%28matrix%282%2C2%2C2%2C-1%2C4%2C-3%29%29%0D%0A=%28matrix%282%2C2%2C-4%2Cz%2C22%2C14%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The -3x becomes 6 since -3x = -3(-2) = 6<BR>\n" );
document.write( "The -9x becomes 18 since -9x = -9(-2) = 18<BR>\n" );
document.write( "Everything else remains the same\r<BR>\n" );
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document.write( "Next, focus on the bottom righthand corners of each matrix.<BR>\n" );
document.write( "The elements in those corners are: -12y, -3, 14<BR>\n" );
document.write( "They produce the equation shown below in which we solve for y\r<BR>\n" );
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document.write( "-12y+(-3) = 14<BR>\n" );
document.write( "-12y-3 = 14<BR>\n" );
document.write( "-12y = 14+3<BR>\n" );
document.write( "-12y = 17<BR>\n" );
document.write( "y = 17/(-12)<BR>\n" );
document.write( "y = -17/12<BR>\n" );
document.write( "We could get an approximation here (roughly -17/12 = -1.41667), but I think it's better to keep it as a fraction.\r<BR>\n" );
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document.write( "Lastly, focus on the upper righthand corners to determine z<BR>\n" );
document.write( "6+(-1) = z<BR>\n" );
document.write( "6-1 = z<BR>\n" );
document.write( "z = 5\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red>x = -2<BR>\n" );
document.write( "y = -17/12<BR>\n" );
document.write( "z = 5</font><BR>\n" );
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