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If the columns are all independent, then there's no way to find unique values for x, y, and z. There are an infinity of answers. If you use 3 columns and want to find a common set of x, y, and z for all three columns, you can do it with the A6:A8 formula:
Excel 2012
<colgroup><col style="width: 25pxpx"><col><col><col><col><col><col><col><col><col><col><col></colgroup><thead>
</thead><tbody>
[TD="align: center"]1[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"][/TD]
[TD="align: right"]1.578947[/TD]
[TD="align: right"]1.833333[/TD]
[TD="align: right"]1.684211[/TD]
[TD="align: right"]1.6875[/TD]
[TD="align: right"]1.380952[/TD]
[TD="align: center"]2[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"][/TD]
[TD="align: right"]1.578947[/TD]
[TD="align: right"]1.833333[/TD]
[TD="align: right"]1.684211[/TD]
[TD="align: right"]1.6875[/TD]
[TD="align: right"]1.380952[/TD]
[TD="align: center"]3[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"][/TD]
[TD="align: right"]1.578947[/TD]
[TD="align: right"]1.833333[/TD]
[TD="align: right"]1.684211[/TD]
[TD="align: right"]1.6875[/TD]
[TD="align: right"]1.380952[/TD]
[TD="align: center"]4[/TD]
[TD="align: right"]30[/TD]
[TD="align: right"]33[/TD]
[TD="align: right"]32[/TD]
[TD="align: right"]27[/TD]
[TD="align: right"]29[/TD]
[TD="align: right"][/TD]
[TD="align: right"]30[/TD]
[TD="align: right"]33[/TD]
[TD="align: right"]32[/TD]
[TD="align: right"]27[/TD]
[TD="align: right"]29[/TD]
[TD="align: center"]5[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
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[TD="align: center"]6[/TD]
[TD="align: right"]-1.4[/TD]
[TD="align: right"][/TD]
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[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]7[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: center"]8[/TD]
[TD="align: right"]3.6[/TD]
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</tbody>
Sheet4
[TABLE="width: 85%"]
<tbody>[TR]
[TD]
Worksheet Formulas[TABLE="width: 100%"]
<thead>[TR="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]
[TH="width: 10px"]Cell[/TH]
[TH="align: left"]Formula[/TH]
[/TR]
</thead><tbody>[TR]
[TH="width: 10px, bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]G1[/TH]
[TD="align: left"]=A$4/(
SUM(A$1:A$3))[/TD]
[/TR]
[TR]
[TH="width: 10px, bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]G4[/TH]
[TD="align: left"]=SUMPRODUCT(
A1:A3,G1:G3)[/TD]
[/TR]
</tbody>[/TABLE]
[/TD]
[/TR]
</tbody>[/TABLE]
[TABLE="width: 85%"]
<tbody>[TR]
[TD]
Array Formulas[TABLE="width: 100%"]
<thead>[TR="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]
[TH="width: 10px"]Cell[/TH]
[TH="align: left"]Formula[/TH]
[/TR]
</thead><tbody>[TR]
[TH="width: 10px, bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=DAE7F5]#DAE7F5[/URL] "]A6:A8[/TH]
[TD="align: left"]{=TRANSPOSE(
MMULT(A4:C4,MINVERSE(A1:C3)))}[/TD]
[/TR]
</tbody>[/TABLE]
Entered with Ctrl+Shift+Enter. If entered correctly, Excel will surround with curly braces {}.
Note: Do not try and enter the {} manually yourself[/TD]
[/TR]
</tbody>[/TABLE]
If you put -1.4, 4, and 3.6 into all three of your equations, they will work. But by looking at 3 different columns, you'll get 3 different values.
If you really do want to want to treat each column independently, then you might be able to add constraints to get an answer. For example, if you set x=y=z, it's easy to solve: x=y=z=30/(8+4+7), which is what I show in column G. Other constraints might be to force x,y,z all positive, and have the smallest sum. It really depends on what you're looking for.