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Algebra 2SuperchallengeLinear Systems & Matrices

Linear Systems & Matrices · Superchallenge problem

Five numbers satisfy the cyclic system

x1+x2+x3=5x2+x3+x4=6x3+x4+x5=2x4+x5+x1=0x5+x1+x2=−4.\begin{aligned} x_1 + x_2 + x_3 &= 5 \\ x_2 + x_3 + x_4 &= 6 \\ x_3 + x_4 + x_5 &= 2 \\ x_4 + x_5 + x_1 &= 0 \\ x_5 + x_1 + x_2 &= -4. \end{aligned}

Find the product x1x2x3x4x5x_1 x_2 x_3 x_4 x_5.