!set n=$counter
math=0
checkfile=exos/checkfile3.proc
question$n=!record 33 of lang/remarks.$taal
#@ Los het stelsel vergelijkingen op.	
exotext=!record 36 of lang/remarks.$taal
#@ <a onmouseover="this.T_WIDTH=260;this.T_OPACITY=80;this.T_BORDERCOLOR='red';this.T_BORDERWIDTH=1;this.T_BGCOLOR='#e8ffff';return escape('Geef je antwoord in zoals:<br><small><em>x=1/3<br>y=3/7<br>z=14</em></small> ')"><font color=blue size=-1><em>Voer je antwoord "wiskundig" in</em></font></a>

!if $level =0
    R=$counter
!else
    R=$level
!endif    
	
!if $variabelen=1
    letters=a,b,c,d,f,x,y,z,p,g,k,t,r,n,m
    letters=!shuffle $letters 
    var1=!item 1 of $letters
    var2=!item 2 of $letters
    var3=!item 3 of $letters
!else
    var1=x
    var2=y
    var3=z
!endif
varlist=$var1,$var2,$var3
mathviewpanel=$module_title:$var1=:$var2=:$var3=:and
!if $breuken=0
    G=!randint 2,25
    GG=!randint 2,25
    GGG=!randint 2,25
    answer$n=$G,$GG,$GGG
    #X => G 
    #Y => GG
    #Z => GGG
    !if $R=1
        #x=a+y
        #y=b+z
        #z=c
        p=!randitem 2,3,4,5,6,7,8
	a=$[$G - $GG]
        b=$[$GG - $GGG]
        c=$[$p*$GGG]
        formula$n=\left\{ \begin{array}{c}$var1 = $a + $var2 \\ \\ $var2 = $b + $var3 \\ \\ $p\cdot $var3 = $c  \end{array}\right. \,\,\, 
        texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
	
    !if $R=2 
        #x+2y=a
        #y-z=b
        #z=c
        p=!randitem 2,3,4,5,6,7,8,-2,-3,-4,-5,-6,-7,-8 	    
           
	a=$[$G + 2*$GG]	
        b=$[$GG - $GGG]
        c=\frac{$[2*$GGG]}{$[2*$p]}
        formula$n=\left\{ \begin{array}{c}$var1 + 2\cdot $var2 = $a \\ \\ $var2 - $var3 = $b \\ \\ \frac{1}{$p}\cdot $var3 = $c \end{array}\right. \,\,\, 
        texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
	
    !if $R=3
        p=!randitem 2,3,4,5,6,7,8 
        #x*y=a
        #y*z=b
        #z=c
        a=$[$G*$GG]
        b=$[$GG*$GGG]
	c=$[$GGG*$p]
        formula$n=\left\{ \begin{array}{c}$var1 \cdot $var2 = $a \\ \\ $var2 \cdot $var3 = $b \\ \\ $p\cdot $var3 = $c \end{array}\right. \,\,\, 
	texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
	
    !if $R>3 
        p=!randitem 2,3,4,5,6,7,8 
        r=!randitem 2,3,4,5,6,7,8
        s=!randitem 2,3,4,5,6,7,8
	!if $r = $[-1*$GG]
	    r=$[$r+1]
	!endif    
	!if $s = $GGG
	    s=$[$s+1]
	!endif    
        #x(y+r)=a
	#y(z-s)=b
        #p(z-x)=c
	a=$[$G*($GG + $r)]
        b=$[$GG*($GGG - $s)]
        c=$[$p*$GGG]
        formula$n=\left\{ \begin{array}{c}$var1 \left( $var2 + $r \right) = $a \\ \\ $var2 \left( $var3 - $s \right) = $b \\ \\ $p \cdot $var3 = $c \end{array}\right. \,\,\,
        texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
!else
    breuk=!shuffle 1/2,1/6,1/4,1/5,2/5,3/2,5/2,1/3,2/3,4/3,3/4,5/4,5/8,3/8,1/8,7/8
    G=!item 1 of $breuk
    GG=!item 2 of $breuk 
    GGG=!item 3 of $breuk
    answer$n=$G,$GG,$GGG
    p=!randitem 2,3,4,5,6,7,8
    #X => G 
    #Y => GG
    #Z => GGG
    !if $R=1
        #x=a+y => a=x-y => a=G-GG
        #y=b+z => b=GG-GGG
        #z=c
	tot=!exec pari printtex($G - $GG)\
	printtex($GG - $GGG)\
	printtex($p*($GGG))
	 	    
        a=!line 1 of $tot
        b=!line 2 of $tot
        c=!line 3 of $tot
        formula$n=\left\{ \begin{array}{c}$var1 = $a + $var2 \\ \\ $var2 = $b + $var3 \\ \\ $p\cdot $var3 = $c  \end{array}\right. \,\,\, 
        texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
	
    !if $R=2 
        #x+2y=a
        #y-z=b
        #z=c
	tot=!exec pari printtex($G + 2*$GG)\
	printtex($GG - $GGG)\
	printtex(2*$GGG/(2*$p))
        
	a=!line 1 of $tot
        b=!line 2 of $tot
        c=!line 3 of $tot	
        formula$n=\left\{ \begin{array}{c}$var1 + 2\cdot $var2 = $a \\ \\ $var2 - $var3 = $b \\ \\ \frac{1}{$p}\cdot $var3 = $c \end{array}\right. \,\,\, 
        texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
	
    !if $R=3
        #x*y=a
        #y*z=b
        #z=c
	tot=!exec pari printtex($G*$GG)\
	printtex($GG*$GGG)\
	printtex(($GGG)*$p)
        
	a=!line 1 of $tot
        b=!line 2 of $tot
        c=!line 3 of $tot
        formula$n=\left\{ \begin{array}{c}$var1 \cdot $var2 = $a \\ \\ $var2 \cdot $var3 = $b \\ \\ $p\cdot $var3 = $c \end{array}\right. \,\,\, 
	texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
	
    !if $R>3 
        p=!randitem 2,3,4,5,6,7,8 
        r=!randitem 2,3,4,5,6,7,8
        s=!randitem 2,3,4,5,6,7,8
	!if $r = $[-1*$GG]
	    r=$[$r+1]
	!endif 
	!if $s = $GGG
	    s=$[$s+1]
	!endif       
        #x(y+r)=a
	#y(z-s)=b
        #px=c
	tot=!exec pari printtex($G*($GG + $r))\
	printtex($GG*($GGG - $s))\
	printtex($p*($GGG))
	a=!line 1 of $tot
        b=!line 2 of $tot
        c=!line 3 of $tot
        formula$n=\left\{ \begin{array}{c}$var1 \left( $var2 + $r \right) = $a \\ \\ $var2 \left( $var3 - $s \right) = $b \\ \\ $p \cdot $var3 = $c \end{array}\right. \,\,\,
        texanswer$n=\left\{ \begin{array}{c} $var1= $G \\ \\ $var2 = $GG \\ \\ $var3 = $GGG \end{array}\right. \,\,\,
     !exit
    !endif
!endif

