rem system of linear equations solver
rem gaussian elimination

print "Linear Equations - Gaussian Elimination"
print "to solve multiple equations of the form"
print "A1*x1+A2*x2+...+An*xn=Constant"
print "enter 'q' at any prompt to quit"
print

dim a(15,16)

for j=1 to 15
 for i=1 to 16
  a(j,i)=0
 next i
next j

input "Number of Equations ";r$
if r$="q" then end
r=val(r$)
print
for j=1 to r
 print "Equation ";j
 for i=1 to r+1
  if i=r+1 then
   print "Constant: "
  else
   print "Coefficient A(";i;")"
  end if
  input " ";a$
  if a$="q" then end
  a(j,i)=val(a$)
 next i
 print
next j
print

rem control loop and matrix check
for j=1 to r
 myi=j
 [loopMyi]
 i = myi
 if a(i,j)<>0 goto [calc]
 myi = myi + 1
 if myi <= r then [loopMyi]

 print "Sorry, no unique solution"
 end

 [calc]
 for k=1 to r+1
  x=a(j,k)
  a(j,k)=a(i,k)
  a(i,k)=x
 next k
 y=1/a(j,j)
 for k=1 to r+1
  a(j,k)=y*a(j,k)
 next k
 for i=1 to r
  if i=j goto [leap]
  y=-1*a(i,j)
  for k=1 to r+1
   a(i,k)=a(i,k)+y*a(j,k)
  next k
  [leap]
 next i
next j
print
for i=1 to r
 ans=int(a(i,r+1)*1000+.5)/1000
print "x";i;"= ";ans
next i
print

end