document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65559>Question 65559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.<BR>\n" );
document.write( "x +5y = 10<BR>\n" );
document.write( "-2x – 10y = -20\r<BR>\n" );
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document.write( "Solve each of the following problems. Be sure to show the equations used for the solution.<BR>\n" );
document.write( "Number problems. Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?\r<BR>\n" );
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document.write( "Business and finance. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 Lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?<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 #46141 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=46141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.<BR>\n" );
document.write( "1st: x +5y = 10<BR>\n" );
document.write( "2nd: -2x – 10y = -20 <BR>\n" );
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document.write( "Let's say you choose to eliminate the x-terms by adding.<BR>\n" );
document.write( "Since the coefficient of the 2nd equation is -2x you want<BR>\n" );
document.write( "to create +2x in the 1st equation; so you multiply both<BR>\n" );
document.write( "sides of the 1st equation by 2 as follows:<BR>\n" );
document.write( "2(x+5y)=2(10)<BR>\n" );
document.write( "3rd:  2x+10y=20<BR>\n" );
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document.write( "Then you add the 2nd and 3rd equations to get:<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "This means equation #2 says the same thing as equation #3.<BR>\n" );
document.write( "The system is dependent. <BR>\n" );
document.write( "This means the two equations are really the same.<BR>\n" );
document.write( "It also means that every point in the line x+5y=10 is a solution <BR>\n" );
document.write( "point for the system of equations.<BR>\n" );
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document.write( "Solve each of the following problems. Be sure to show the equations used for the solution.<BR>\n" );
document.write( "Number problems. Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?<BR>\n" );
document.write( "Let number of nickels be \"x\"; Value of these is 10x cents<BR>\n" );
document.write( "Number of dimes is \"50-x\"; Value of these is 10(50-x)=(500-10x)cents<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "value + value= 350cents<BR>\n" );
document.write( "10x+500-10x=350<BR>\n" );
document.write( "0=-150<BR>\n" );
document.write( "This is a contradiction.<BR>\n" );
document.write( "The system is inconsistent<BR>\n" );
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document.write( "Business and finance. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 Lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?<BR>\n" );
document.write( "Amount of $9 is \"x\" lbs; Value is 9x dollars<BR>\n" );
document.write( "Amount of $12 is \"100-x\"; Value is 12(100-x)=1200-12x dollars<BR>\n" );
document.write( "Amount of mixture is 100 lb; Value is 11.25(100)=1125 dollars<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "value + value = 1125 dollars<BR>\n" );
document.write( "9x+1200-12x=1125<BR>\n" );
document.write( "-3x=-75<BR>\n" );
document.write( "x=25 lb (amount of $9 coffee)<BR>\n" );
document.write( "100-x=75 lb (amount of $12 coffee)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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