document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147355>Question 147355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I dont know what Im doing wrong I need help please. Here is the question:  One year ago you invested $4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest.  The interest you earned after one year is $193.  You remembered you invested three times as much in the 4% account than you did the 3.25% account. How much did you invest in each type of account?   This is what i have so far, I dont think its right.<BR>\n" );
document.write( "x   +   y   +    Z   =  4300<BR>\n" );
document.write( "325x + 400Y  + 575z  = 19300<BR>\n" );
document.write( "Y=3x<BR>\n" );
document.write( "x +  (3x)  +    Z  =  4300<BR>\n" );
document.write( "4x  +  z  = 4300<BR>\n" );
document.write( "325x  + 400 (3x)  + z  =19300<BR>\n" );
document.write( "1525x +575z = 19300\r<BR>\n" );
document.write( "\n" );
document.write( "(-575) 4x + z = 4300 (-575)<BR>\n" );
document.write( "-2300x - 575z  =-2472500<BR>\n" );
document.write( "1525x  + 575z  = 19300<BR>\n" );
document.write( "-775x = -2453200<BR>\n" );
document.write( "x=3165.4  then when I do 3 times x to get y  it doesnt fit with the total of 4300.  I dont know please help me thank you.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107729 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=107729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + w + y = 4300<BR>\n" );
document.write( "0.0325x + 0.04w + 0.0575y = 193<BR>\n" );
document.write( "3.25x + 4(3x) + 05.75y = 19300\r<BR>\n" );
document.write( "\n" );
document.write( "4x + y = 4300<BR>\n" );
document.write( "15.25x + 5.75y = 19300\r<BR>\n" );
document.write( "\n" );
document.write( "Using substitution:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solving_linear_system_by_substitution.solver>Solving a linear system of equations by subsitution</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Lets start with the given system of linear equations<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ay=4300 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ay=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Solve for y for the first equation <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ay=4300-4%2Ax ALIGN=MIDDLE  ALT=\"1%2Ay=4300-4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax ALIGN=MIDDLE  ALT=\"4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284300-4%2Ax%29 ALIGN=MIDDLE  ALT=\"y=%284300-4%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 1. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Which breaks down and reduces to <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4300-4%2Ax ALIGN=MIDDLE  ALT=\"y=4300-4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we've fully isolated y<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since y equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4300-4%2Ax ALIGN=MIDDLE  ALT=\"4300-4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can substitute the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4300-4%2Ax ALIGN=MIDDLE  ALT=\"4300-4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > into y of the 2nd equation. This will eliminate y so we can solve for x.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ahighlight%28%284300-4%2Ax%29%29=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ahighlight%28%284300-4%2Ax%29%29=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4300-4%2Ax ALIGN=MIDDLE  ALT=\"4300-4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since this eliminates y, we can now solve for x.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2A%284300%29%2B5.75%28-4%29x=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2A%284300%29%2B5.75%28-4%29x=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute 5.75 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4300-4%2Ax ALIGN=MIDDLE  ALT=\"4300-4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B24725-23%2Ax=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B24725-23%2Ax=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B24725-23%2Ax=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B24725-23%2Ax=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax-23%2Ax=19300-24725 ALIGN=MIDDLE  ALT=\"15.25%2Ax-23%2Ax=19300-24725\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24725 ALIGN=MIDDLE  ALT=\"24725\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax-23%2Ax=-5425 ALIGN=MIDDLE  ALT=\"15.25%2Ax-23%2Ax=-5425\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7.75%2Ax=-5425 ALIGN=MIDDLE  ALT=\"-7.75%2Ax=-5425\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine the terms on the left side.  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F-7.75%29%28-7.75%2F1%29%29x=%28-5425%2F1%29%281%2F-7.75%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F-7.75%29%28-7.75%2F1%29%29x=%28-5425%2F1%29%281%2F-7.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F-7.75 ALIGN=MIDDLE  ALT=\"1%2F-7.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7.75%2F1 ALIGN=MIDDLE  ALT=\"-7.75%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and isolate x<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So when we multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5425%2F1 ALIGN=MIDDLE  ALT=\"-5425%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F-7.75 ALIGN=MIDDLE  ALT=\"1%2F-7.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > (and simplify) we get <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---------------------------------One answer<BR>\n" );
document.write( "  <BR>\n" );
document.write( "   Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" >, lets substitute that in for x to solve for y<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%28700%29%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%28700%29%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the 2nd equation <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10675%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"10675%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.75%2Ay=19300-10675 ALIGN=MIDDLE  ALT=\"5.75%2Ay=19300-10675\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10675 ALIGN=MIDDLE  ALT=\"10675\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.75%2Ay=8625 ALIGN=MIDDLE  ALT=\"5.75%2Ay=8625\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F5.75%29%285.75%29%29%2Ay=%288625%2F1%29%281%2F5.75%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F5.75%29%285.75%29%29%2Ay=%288625%2F1%29%281%2F5.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5.75 ALIGN=MIDDLE  ALT=\"1%2F5.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out 5.75 on the left side.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8625%2F5.75 ALIGN=MIDDLE  ALT=\"y=8625%2F5.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the terms on the right side<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So this is the other answer<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---------------------------------Other answer<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So our solution is <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  which can also look like <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Notice if we graph the equations (if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ay=4300 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ay=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  we get <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+600%2C+-710%2C+710%2C+-1510%2C+1510%2C%0D%0A++++graph%28+500%2C+600%2C+-710%2C+710%2C+-1510%2C+1510%2C+%284300-4%2Ax%29%2F1%2C+%2819300-15.25%2Ax%29%2F5.75+%29%2C%0D%0A++++blue%28++circle%28+700%2C+1500%2C+9.46666666666667+%29+%29+%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ay=4300 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ay=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  and we can see that the two equations intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  -----------------------------------------------------------------------------------------------<BR>\n" );
document.write( "  Check:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >) into the system of equations<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now plug those values into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ay=4300 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ay=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28700%29%2B1%2A%281500%29=4300 ALIGN=MIDDLE  ALT=\"4%2A%28700%29%2B1%2A%281500%29=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2800%2B1500=4300 ALIGN=MIDDLE  ALT=\"2800%2B1500=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4300=4300 ALIGN=MIDDLE  ALT=\"4300=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4300=4300 ALIGN=MIDDLE  ALT=\"4300=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. Since this equation is true the solution works.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ay=4300 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ay=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now plug those values into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2A%28700%29%2B5.75%2A%281500%29=19300 ALIGN=MIDDLE  ALT=\"15.25%2A%28700%29%2B5.75%2A%281500%29=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=700 ALIGN=MIDDLE  ALT=\"x=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1500 ALIGN=MIDDLE  ALT=\"y=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10675%2B8625=19300 ALIGN=MIDDLE  ALT=\"10675%2B8625=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19300=19300 ALIGN=MIDDLE  ALT=\"19300=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19300=19300 ALIGN=MIDDLE  ALT=\"19300=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. Since this equation is true the solution works.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the solution (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700 ALIGN=MIDDLE  ALT=\"700\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfies the system of equations<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2B1%2Ay=4300 ALIGN=MIDDLE  ALT=\"4%2Ax%2B1%2Ay=4300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.25%2Ax%2B5.75%2Ay=19300 ALIGN=MIDDLE  ALT=\"15.25%2Ax%2B5.75%2Ay=19300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  this verifies our answer.<BR>\n" );
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document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "So x = $700<BR>\n" );
document.write( "w = 3x = $2100<BR>\n" );
document.write( "y = $1500\r<BR>\n" );
document.write( "\n" );
document.write( "Verify your answers. Does 0.0325(700 + 0.04(2100) + 0.057(1500) = 193?\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );