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Solve for x, y, z
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y=-3x-5z-10w+2
Solve 3x+y+5z+10w=2 for y.
x-3x-5z-10w+2+2z+4w=0 x-2\left(-3x-5z-10w+2\right)+4z+w=3
Substitute -3x-5z-10w+2 for y in the second and third equation.
x=-\frac{3}{2}z-3w+1 z=\frac{1}{2}-\frac{1}{2}x-\frac{3}{2}w
Solve these equations for x and z respectively.
z=\frac{1}{2}-\frac{1}{2}\left(-\frac{3}{2}z-3w+1\right)-\frac{3}{2}w
Substitute -\frac{3}{2}z-3w+1 for x in the equation z=\frac{1}{2}-\frac{1}{2}x-\frac{3}{2}w.
z=0
Solve z=\frac{1}{2}-\frac{1}{2}\left(-\frac{3}{2}z-3w+1\right)-\frac{3}{2}w for z.
x=-\frac{3}{2}\times 0-3w+1
Substitute 0 for z in the equation x=-\frac{3}{2}z-3w+1.
x=1-3w
Calculate x from x=-\frac{3}{2}\times 0-3w+1.
y=-3\left(1-3w\right)-5\times 0-10w+2
Substitute 1-3w for x and 0 for z in the equation y=-3x-5z-10w+2.
y=-1-w
Calculate y from y=-3\left(1-3w\right)-5\times 0-10w+2.
x=1-3w y=-1-w z=0
The system is now solved.