System of Linear Equations Integer Solutions (J…

Determinants

Medium

System of Linear Equations Integer Solutions

Let the system of equations
x + 5y –z = 1
4x + 3y –3z = 7
24x + y + λz = μ
λ, $\mu \in R$ , have infinitely many solutions. Then the number of the solutions of this system,
If x, y, z are integers and satisfy $7 \leqslant x + y + z \leqslant 77$ , is

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