Solve for x, y, z
x=-4
y=6
z=1
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z=-3x-2y+1
Solve 3x+2y+z=1 for z.
5x+3y+4\left(-3x-2y+1\right)=2 x+y-\left(-3x-2y+1\right)=1
Substitute -3x-2y+1 for z in the second and third equation.
y=-\frac{7}{5}x+\frac{2}{5} x=-\frac{3}{4}y+\frac{1}{2}
Solve these equations for y and x respectively.
x=-\frac{3}{4}\left(-\frac{7}{5}x+\frac{2}{5}\right)+\frac{1}{2}
Substitute -\frac{7}{5}x+\frac{2}{5} for y in the equation x=-\frac{3}{4}y+\frac{1}{2}.
x=-4
Solve x=-\frac{3}{4}\left(-\frac{7}{5}x+\frac{2}{5}\right)+\frac{1}{2} for x.
y=-\frac{7}{5}\left(-4\right)+\frac{2}{5}
Substitute -4 for x in the equation y=-\frac{7}{5}x+\frac{2}{5}.
y=6
Calculate y from y=-\frac{7}{5}\left(-4\right)+\frac{2}{5}.
z=-3\left(-4\right)-2\times 6+1
Substitute 6 for y and -4 for x in the equation z=-3x-2y+1.
z=1
Calculate z from z=-3\left(-4\right)-2\times 6+1.
x=-4 y=6 z=1
The system is now solved.
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