document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=822251>Question 822251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The math club is selling pizza and lemonade to raise money for a field trip. the trip will cost $450  <BR>\n" );
document.write( "If they sell pizza for $1 per slice for and lemonade$2 a bottle and sold 190 items. How many of each did they sell?\r<BR>\n" );
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document.write( "The sum of 2 numbers is 87. the first number is 3 more than twice the second number.\r<BR>\n" );
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document.write( "2x+3y=12<BR>\n" );
document.write( "X=y+4  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494732 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=494732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "you have 3 different problems here:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "first problem (pizza and lemonade): <BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + 2y = 450<BR>\n" );
document.write( "x + y = 190<BR>\n" );
document.write( "y = 190 - x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + 2(190 - x) = 450<BR>\n" );
document.write( "x + 380 - 2x = 450<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = pizza slices sold = -70 (nobody can sell a negative number of pizza slices)<BR>\n" );
document.write( "y = lemonades sold = 260<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "the problem statement contains an error because the equations yield a nonsensical solution.<BR>\n" );
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document.write( "second problem:<BR>\n" );
document.write( "x + y = 87<BR>\n" );
document.write( "x = 2y + 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + y = 87<BR>\n" );
document.write( "x - 2y = 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solve by matrix method (the below solver uses the matrix method):<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above standard form linear equations in to this solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "x= 59<BR>\n" );
document.write( "y= 28<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solve by elimination:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + y = 87<BR>\n" );
document.write( "-x + 2y = -3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "add:<BR>\n" );
document.write( "3y = 84<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer (same as obtained by the matrix method above):<BR>\n" );
document.write( "y = 28<BR>\n" );
document.write( "x = 59<BR>\n" );
document.write( "---<BR>\n" );
document.write( "third problem:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2x + 3y = 12<BR>\n" );
document.write( "x = y + 4 <BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2x + 3y = 12<BR>\n" );
document.write( "x - y = 4 <BR>\n" );
document.write( "---<BR>\n" );
document.write( "solve by matrix method (the below solver uses the matrix method):<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above standard form linear equations in to this solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "x= 4.8<BR>\n" );
document.write( "y= 0.8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solve by elimination:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2x + 3y = 12<BR>\n" );
document.write( "-2x + 2y = -8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "add:<BR>\n" );
document.write( "5y = 4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer (same as obtained by the matrix method above):<BR>\n" );
document.write( "y = 4/5 = 0.8<BR>\n" );
document.write( "x = 4.8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );