ALINEARSYS

[Xlambda]

ALINEARSYS solves any system of linear equations. Thought to put some of text manipulation formulas to work for a higher purpose. ?
calls : AFLATTEN , ASPLIT , ATRIM , AREPLACE , AREMOVE , T_CHARS

=LAMBDA(ec,
    LET(d,"|",r,ROWS(ec),ae,SWITCH(LEFT(ec,1),"+","","-","","+")&ec,es,ASPLIT(ae,"="),e,INDEX(es,,1),n,INDEX(es,,2),ea,ASPLIT(ATRIM(AREPLACE(e,{"+";"-"},{"|+";"|-"}),d,),d),c,COLUMNS(ea),
       f,AFLATTEN(ea),l,LEN(f),fr,AREMOVE(f,T_CHARS(,-1,),d),rf,SEARCH(d,fr),fs,IF(ISERR(rf),IF(l=0,fr,fr&d),fr),sf,SEARCH(d,fs),ce,MID(f,1,sf-1),
       cf,IFERROR(--SWITCH(ce,"-",-1,"+",1,ce),0),v,IFERROR(MID(f,sf,l-sf+1),""),uv,SORT(UNIQUE(FILTER(v,v<>""))),tv,TRANSPOSE(uv),
       q,QUOTIENT(SEQUENCE(r*c)-1,c)+1,x,XMATCH(v,tv),s,(q-1)*r+x,m,IFNA(XLOOKUP(SEQUENCE(r,r),s,cf),0),mi,MINVERSE(m),rs,MMULT(mi,n),
       cx,OR(AREMOVE(LOWER(ec),T_CHARS(1,-1,"+-.="),"")<>""),ca,r<>ROWS(uv),cb,AND(ISNUMBER(n)),cc,AND(ISERR(mi)),
       IFS(cx,"check syntax",ca,"check variables",NOT(cb),"only nrs after =",cc,"no solutions",TRUE,CHOOSE({1,2},uv&" =",rs))
    )
)

LAMBDA 7.0.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S
1	sample				=ALINEARSYS(A2:A12)					=ALINEARSYS(H2:H5)					=ALINEARSYS(M2:M5)
2	x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11=100				x1 =	9.901271973		-b-c+d=-4		a =	2.82352941		x=2		a =	-3
3	-2x3+4x6-2x11=12				x10 =	10.78741129		b+c+a+d=10		b =	2.52941176		-a=3		b =	1
4	4x2-3x11+2x9-4x5=6				x11 =	-34.00819959		c-2d+2a-b=3		c =	3.05882353		b=1		c =	-4
5	-2x10+2x1+0.7x4+x8=12				x2 =	-15.81144776		-2c+2d+3a-b=3		d =	1.58823529		-c=4		x =	2
6	x5-2x7+x2=9				x3 =	-19.90090621				sum check	10
7	x5+2x3-x9+3x7-2x6=15				x4 =	-20.11349492
8	2x8-x10-2x1+x4=5				x5 =	55.44094879				=ALINEARSYS(H9:H12)					=ALINEARSYS(M9:M11)
9	1.5x7-2x2+3x4-1.2x6=23				x6 =	-23.9545529		2ax3-2ax2+ax1=10		ax1 =	84.9473684		2x11-x22+2x33=-3		x11 =	2
10	x8-2x3+x10-x5=23				x7 =	15.31475052		-ax4+.5ax2=-2		ax2 =	-17.789474		x11+x22-x33=6		x22 =	1
11	-x9+2x10+x1-2x11=5				x8 =	27.85172508		.33ax3+.25ax1=3		ax3 =	-55.263158		x11+2x22-4x33=16		x33 =	-3
12	x3-x4+x10=11				x9 =	94.49249372		ax1+ax3+ax4+ax2=5		ax4 =	-6.8947368
13										sum check	5
14						=SUM(F2:F12)
15					check	100
16											=ALINEARSYS(J17:J18)					=ALINEARSYS(O17:O18)
17	Syntax rules:	No variables after "=" sign								a-2*b=3	check syntax				a-2b=3	a =	7
18		If ecuation starts with + or - use " ' " as first char. '-2x+….								a+b=9					a+b=9	b =	2
19		0.5 instead of 1/2								(* char)
20
21			=ALINEARSYS(B22:B24)				=ALINEARSYS(F22:F24)				=ALINEARSYS(J22:J23)				=ALINEARSYS(M22:M23)
22	Error debug.	x+y-z=5	no solutions			x+y-z=5	no solutions			x+y=2x	only nrs after =		x+y+z=3		check variables
23		y-5z=8				y-5z=8				x-y=1			x-y=1
24		y-5z=-1				2x+2y-2z=10				(=2x)			(3 variables,only 2 ec)
25		(2nd and 3rd ec inconsistent)				(1st and 3rd, same ecuation, infinite solutions)
26
ALINEARSYS post

Cell Formulas
Range	Formula
E1,O21,G21,K21,C21,P16,K16,F14,O8,J8,O1,J1	E1	=FORMULATEXT(E2)
E2:F12	E2	=ALINEARSYS(A2:A12)
J2:K5,J9:K12,O2:P5	J2	=ALINEARSYS(H2:H5)
K6,K13	K6	=SUM(K2:K5)
O9:P11	O9	=ALINEARSYS(M9:M11)
F15	F15	=SUM(F2:F12)
K17,K22,P17:Q18	K17	=ALINEARSYS(J17:J18)
C22,G22	C22	=ALINEARSYS(B22:B24)
O22	O22	=ALINEARSYS(M22:M23)
Dynamic array formulas.