document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75561>Question 75561</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131482874/algebrahomeworkh>Beginning Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help!!!  I don't understand any of this.  Any assistance you can provide will be greatly appreciated.  Thanks in advance.\r<BR>\n" );
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document.write( "PG. 483<BR>\n" );
document.write( "Find the solution to each system of equations by the substitution method.  Check your answers.  Place your solution in the form (x,y), (a,b), (p,q), or (s,t).\r<BR>\n" );
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document.write( "(2.) x = 4 - 4y                (6.) 4x + 2y = 4<BR>\n" );
document.write( "  -x + 2y = 2                   3x +  y = 4\r<BR>\n" );
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document.write( "PG. 490<BR>\n" );
document.write( "Find the solution by the addition method.  Check your answers.\r<BR>\n" );
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document.write( "(6.) -x + y = 2                (8.) 2x + y = 4          (14.) 5x - 3y = 14      <BR>\n" );
document.write( "    x + y = 4                   3x - 2y = -1            2x - y = 6\r<BR>\n" );
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document.write( "PG. 504<BR>\n" );
document.write( "Solve using two equations with two variables.\r<BR>\n" );
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document.write( "(4.) El Segundo High School put on their annual musical.  The students sold 650 tickets for a value of $4375.  If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54248 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=54248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PG. 483<BR>\n" );
document.write( "Find the solution to each system of equations by the substitution method.  Check your answers.  Place your solution in the form (x,y), (a,b), (p,q), or (s,t).\r<BR>\n" );
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document.write( "(2.) x = 4 - 4y                <BR>\n" );
document.write( "  -x + 2y = 2  <BR>\n" );
document.write( "Substitute x=4-4y in the second equation and solve for y:<BR>\n" );
document.write( "-(4-4y)+2y=2<BR>\n" );
document.write( "-4+4y+2y=2<BR>\n" );
document.write( "-4+6y=2<BR>\n" );
document.write( "4-4+6y=2+4<BR>\n" );
document.write( "6y=6<BR>\n" );
document.write( "6y/6=6/6<BR>\n" );
document.write( "y=1<BR>\n" );
document.write( "Now substitute y=1 in the first equation and solve for x.<BR>\n" );
document.write( "x=4-4(1)<BR>\n" );
document.write( "x=4-4<BR>\n" );
document.write( "x=0<BR>\n" );
document.write( "The solution is (x,y)=(0,1)<BR>\n" );
document.write( "You check by substituting x=0 and y=1 into both equations and see if they balance:<BR>\n" );
document.write( "0=4-4(1)<BR>\n" );
document.write( "0=4-4<BR>\n" );
document.write( "0=0 the first one checks<BR>\n" );
document.write( "-(0)+2(1)=2<BR>\n" );
document.write( "0+2=2<BR>\n" );
document.write( "2=2 The second one checks as well, so you're right.                 <BR>\n" );
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document.write( "(6.) 4x + 2y = 4<BR>\n" );
document.write( "3x +  y = 4<BR>\n" );
document.write( "Solve the second equation for y.<BR>\n" );
document.write( "3x-3x+y=4-3x<BR>\n" );
document.write( "y=4-3x<BR>\n" );
document.write( "Now substitute y=4-3x into the first equation and solve for x.<BR>\n" );
document.write( "4x+2(4-3x)=4<BR>\n" );
document.write( "4x+8-6x=4<BR>\n" );
document.write( "-2x+8=4<BR>\n" );
document.write( "-2x+8-8=4-8<BR>\n" );
document.write( "-2x=-4<BR>\n" );
document.write( "-2x/-2=-4/-2<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "Now substitute x=2 into the second equation and solve for y.<BR>\n" );
document.write( "3(2)+y=4<BR>\n" );
document.write( "6+y=4<BR>\n" );
document.write( "6-6+y=4-6<BR>\n" );
document.write( "y=-2<BR>\n" );
document.write( "The solution is (x,y)=(2,-2)<BR>\n" );
document.write( "Check by substituting x=2 and y=-2 in both equations and see if they balance.<BR>\n" );
document.write( "4(2)+2(-2)=4<BR>\n" );
document.write( "8-4=4<BR>\n" );
document.write( "4=4  First equation checks out.<BR>\n" );
document.write( "3(2)+(-2)=4<BR>\n" );
document.write( "6-2=4<BR>\n" );
document.write( "4=4  This one checks too.<BR>\n" );
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document.write( "Find the solution by the addition method.  Check your answers.\r<BR>\n" );
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document.write( "(6.) -x + y = 2  Add the two equations together and the x's are eliminated                               <BR>\n" );
document.write( "    x + y = 4    <BR>\n" );
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document.write( "0+2y=6  solve for y<BR>\n" );
document.write( "2y=6<BR>\n" );
document.write( "2y/2=6/2<BR>\n" );
document.write( "y=3<BR>\n" );
document.write( "Substitute y=3 into either equation and solve for x.<BR>\n" );
document.write( "x+(3)=4<BR>\n" );
document.write( "x+3-3=4-3<BR>\n" );
document.write( "x=1<BR>\n" );
document.write( "The solution is (x,y)=(1,3)  I'll leave the rest for you to check.  <BR>\n" );
document.write( "                          <BR>\n" );
document.write( "(8.) 2x + y = 4 <BR>\n" );
document.write( "3x - 2y = -1 <BR>\n" );
document.write( "If you multiply the first equation by 2 the y's will be eliminated when you add the equations. 2(2x+y)=2(4)--->4x+2y=8<BR>\n" );
document.write( "4x+2y=8<BR>\n" );
document.write( "3x-2y=-1<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "7x+0=7 solve for x<BR>\n" );
document.write( "7x=7<BR>\n" );
document.write( "7x/7=7/7<BR>\n" );
document.write( "x=1<BR>\n" );
document.write( "Substitute x=1 into either equation and solve for y.<BR>\n" );
document.write( "2(1)+y=4<BR>\n" );
document.write( "2+y=4<BR>\n" );
document.write( "2-2+y=4-2<BR>\n" );
document.write( "y=2<BR>\n" );
document.write( "The solution is (x,y)=(1,2)  Don't forget to check it.<BR>\n" );
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document.write( "(14.) 5x - 3y = 14<BR>\n" );
document.write( "2x - y = 6<BR>\n" );
document.write( "Multiply the second equation by -3 and the y's will be eliminated when you add the equations. -3(2x-y)=-3(6)---->-6x+3y=-18<BR>\n" );
document.write( "5x-3y=14<BR>\n" );
document.write( "-6x+3y=-18<BR>\n" );
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document.write( "-x+0=-4<BR>\n" );
document.write( "-x/-1=-4/-1<BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "Substitute that into either equation:<BR>\n" );
document.write( "2(4)-y=6<BR>\n" );
document.write( "8-y=6<BR>\n" );
document.write( "8-8-y=6-8<BR>\n" );
document.write( "-y=-2<BR>\n" );
document.write( "-y/-1=-2/-1<BR>\n" );
document.write( "y=2<BR>\n" );
document.write( "The solution is (x,y)=(4,2)  Don't forget to check it.<BR>\n" );
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document.write( "PG. 504<BR>\n" );
document.write( "Solve using two equations with two variables.\r<BR>\n" );
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document.write( "(4.) El Segundo High School put on their annual musical.  The students sold 650 tickets for a value of $4375.  If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?<BR>\n" );
document.write( "Let orchestra seats be: x<BR>\n" );
document.write( "Let balcony seats be: y<BR>\n" );
document.write( "Then the amount of tickets sold is represented by: x+y=650<BR>\n" );
document.write( "The amount of money made on the tickets is: 7.50x+3.50y=4375<BR>\n" );
document.write( "You can use either substitution or elimination to solve, I think in this case, substitution is easiest.<BR>\n" );
document.write( "x+y=650<BR>\n" );
document.write( "x-x+y=650-x<BR>\n" );
document.write( "y=650-x  substitute into the second equation.<BR>\n" );
document.write( "7.50x+3.50(650-x)=4375<BR>\n" );
document.write( "10(7.50x)+10(3.50)(650-x)=10(4375)<BR>\n" );
document.write( "75x+35(650-x)=43750<BR>\n" );
document.write( "75x+22750-35x=43750<BR>\n" );
document.write( "40x+22750=43750<BR>\n" );
document.write( "40x+22750-22750=43750-22750<BR>\n" );
document.write( "40x=21000<BR>\n" );
document.write( "40x/40=21000/40<BR>\n" );
document.write( "x=525<BR>\n" );
document.write( "Substitute that into the first equation<BR>\n" );
document.write( "525+y=650<BR>\n" );
document.write( "525-525+y=650-525<BR>\n" );
document.write( "y=125<BR>\n" );
document.write( "Orchestra seats x=525<BR>\n" );
document.write( "Balcony seats y=125<BR>\n" );
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document.write( "Happy Calculating!!!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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