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Algebra 2SuperchallengeLinear Systems & Matrices

Linear Systems & Matrices · Superchallenge problem

How many solutions (x,y,z,w)(x, y, z, w) in nonnegative integers does the system

x+y+z+w=20x+2y+3z+4w=50\begin{aligned} x + y + z + w &= 20 \\ x + 2y + 3z + 4w &= 50 \end{aligned}

have?