!set n=$teller

bewerking=bewerking2.proc

!if $taal=nl
    nivo_title=Los het volgende stelsel vergelijking op<br><font color=$fontcolor3>Twee vergelijkingen met twee onbekenden</font>
!else
    nivo_title=Solve the set of equations <br><font color=$fontcolor3>Two equations with two variables</font>
!endif

!if $graad =0
    R=$teller
!else
    R=$graad
!endif    

!if $variabelen=1
    letters=a,b,c,d,f,x,y,z,p,g,k,t,r,n,m
    letters=!shuffle $letters 
    X$n=!item 1 of $letters
    Y$n=!item 2 of $letters
!else
    X$n=x
    Y$n=y
!endif

a=!randitem 2,3,4,5,6,7,8
b=!randitem 2,3,4,5,6,7,8
!if $breuken=0
    G$n=!randitem 1,2,4,6,8,10,11,13
    GG$n=!randitem 3,5,7,9,12,14
    # X => G 
    # Y => GG
    !if $R=1
        # x=by => b=x/y => G/GG
        # x-y=d => d=G-GG
	bb=!exec pari printtex($(G$n)/$(GG$n))\
	printtex($(G$n)-$(GG$n))
        b=!line 1 of $bb
        d=!line 2 of $bb	
	som$n=\left\{ \begin{array}{c}$(X$n) = $b \cdot $(Y$n) \\ \\ $(X$n) - $(Y$n) = $d \end{array}\right. 	   
	extra$n=\left\{ \begin{array}{c} $(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif
	
    !if $R=2 
	# X => G 
	# Y => GG
        # bx=y => b=y/x => GG/G
        # x-y=d => d=G-GG
        bb=!exec pari printtex($(GG$n)/$(G$n))\
	printtex($(G$n)-$(GG$n))
        b=!line 1 of $bb
        d=!line 2 of $bb
        som$n=\left\{ \begin{array}{c}$b \cdot $(X$n) = $(Y$n) \\ \\  $(X$n) - $(Y$n) = $d \end{array}\right.
        extra$n=\left\{ \begin{array}{c}$(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif
	
    !if $R=3 
	# X => G 
	# Y => GG
        # x=by => b=x/y => b=G/GG
        # ax-y=d 
        bb=!exec pari printtex($(G$n)/$(GG$n))\
	printtex($a*$(G$n)-$(GG$n))
        b=!line 1 of $bb
        d=!line 2 of $bb
        som$n=\left\{ \begin{array}{c}$(X$n) = $b\cdot $(Y$n) \\ \\ $a\cdot $(X$n) - $(Y$n) = $d \end{array}\right.
        extra$n=\left\{ \begin{array}{c}$(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif    
    
    !if $R>3 
	# X => G 
	# Y => GG
	# ax+by=c 
        # x+y=d 
	!if $a=$b
	    a=$[$a+1]
	!endif    
        c=$[$a*$(G$n) + $b*$(GG$n)]
        d=$[$(G$n) + $(GG$n)]
        som$n=\left\{ \begin{array}{c} $a\cdot $(X$n) + $b\cdot $(Y$n) = $c \\ \\ $(X$n) + $(Y$n) = $d \end{array}\right. 	
        extra$n=\left\{ \begin{array}{c}$(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif

!else
    breuk=!shuffle 1/2,1/4,1/5,2/5,3/2,5/2,1/3,2/3,4/3,3/4,5/4,5/8,3/8,1/8,7/8
    G$n=!item 1 of $breuk
    GG$n=!item 2 of $breuk 
    # X => G 
    # Y => GG
    !if $R=1
        # x = by => b=x/y => G/GG
        # x-y=d => d=G-GG
	bb=!exec pari printtex(($(G$n))/($(GG$n)))\
	printtex(($(G$n))-($(GG$n)))
        b=!line 1 of $bb
	d=!line 2 of $bb
	som$n=\left\{ \begin{array}{c}$(X$n) = $b \cdot $(Y$n)  \\ \\ $(X$n) - $(Y$n) = $d \end{array}\right. 	   
	extra$n=\left\{ \begin{array}{c} $(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif
	
    !if $R=2 
	# X => G 
        # Y => GG
        # bx=y => b=y/x => b= GG/G
        # x-y=d => d= G-GG
        bb=!exec pari printtex(($(GG$n))/($(G$n)))\
	printtex($(G$n)-$(GG$n))
        b=!line 1 of $bb
        d=!line 2 of $bb
        som$n=\left\{ \begin{array}{c}$b \cdot $(X$n) = $(Y$n) \\ \\  $(X$n) - $(Y$n) = $d \end{array}\right.
        extra$n=\left\{ \begin{array}{c}$(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif
	
    !if $R=3 
        # X => G 
        # Y => GG
        # x=by => b=x/y => b= G/GG 
        # ax-y=d => d=a*G - GG
        bb=!exec pari printtex(($(G$n))/($(GG$n)))\
	printtex($a*$(G$n)-$(GG$n))
	b=!line 1 of $bb
        d=!line 2 of $bb
        som$n=\left\{ \begin{array}{c}$(X$n) = $b\cdot $(Y$n) \\ \\ $a\cdot $(X$n) - $(Y$n) = $d \end{array}\right.
        extra$n=\left\{ \begin{array}{c}$(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif    
    
    !if $R>3 
        # X => G 
        # Y => GG
	# ax+by=c => c= a*G + b*GG
        # x+y=d => d=G + GG
	!if $a=$b
	    a=$[$a+1]
	!endif    
	bb=!exec pari printtex($a*($(G$n)) + $b*($(GG$n)))\
	printtex($(G$n) + $(GG$n))
        c=!line 1 of $bb
        d=!line 2 of $bb
        som$n=\left\{ \begin{array}{c} $a\cdot $(X$n) + $b\cdot $(Y$n) = $c \\ \\ $(X$n) + $(Y$n) = $d \end{array}\right. 	
        extra$n=\left\{ \begin{array}{c}$(X$n)= $(G$n) \\ \\ $(Y$n) = $(GG$n) \end{array}\right.
     !exit
    !endif

!endif