View of /trunk/NationalProblemLibrary/ASU-topics/set119LinearSystems/p5.pg

    1 ## DESCRIPTION
    2 ## Systems of Linear Equations
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Algebra' 'Linear Equations')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Systems of Equations and Inequalities')
   10 ## DBsection('Systems of Linear Equations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $x=random(-3,3,1);
   34 $y=random(-3,3,1);
   35 $b1 = 3*$x + 2*$y ;
   36 $b2 = $x - 2*$y;
   37 BEGIN_TEXT
   38 Solve the system
   39 \[
   40 \begin{array}{l}
   41         3x+2y = $b1, \\
   42         x-2y = $b2. \\
   43 \end{array}
   44 \]
   45 If the system has infinitely many solutions, express your answer in
   46 the form \(x=x\) and
   47 \(y\) as a function of \(x\)
   48 $BR
   49 Your answer is
   50 $BR
   51 \(x=\) \{ans_rule(25) \}
   52 $BR
   53 \(y=\) \{ans_rule(25) \}
   54 $BR
   55 END_TEXT
   56 
   57 $ans1 = $x;
   58 $ans2 = $y;
   59 ANS(num_cmp($ans1));
   60 ANS(num_cmp($ans2));
   61 
   62 ENDDOCUMENT();        # This should be the last executable line in the problem.