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What is the dimension of the set of points in 6-dimensional space for which x 1 +x 2 +x 3 +x 4 +x 5 +x

What is the dimension of the set of points in 6-dimensional space for which

x₁+x₂+x₃+x₄+x₅+x₆=12 and

x₁+2x₂+3x₃+4x₄+5x₅+6x₆= 50?

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