Solve for x, y, z
x=2
y=3
z=-1
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z=2x-3y+4
Solve 2x-3y-z=-4 for z.
x+2y+2\left(2x-3y+4\right)=6 3x+2y+2x-3y+4=11
Substitute 2x-3y+4 for z in the second and third equation.
y=\frac{5}{4}x+\frac{1}{2} x=\frac{7}{5}+\frac{1}{5}y
Solve these equations for y and x respectively.
x=\frac{7}{5}+\frac{1}{5}\left(\frac{5}{4}x+\frac{1}{2}\right)
Substitute \frac{5}{4}x+\frac{1}{2} for y in the equation x=\frac{7}{5}+\frac{1}{5}y.
x=2
Solve x=\frac{7}{5}+\frac{1}{5}\left(\frac{5}{4}x+\frac{1}{2}\right) for x.
y=\frac{5}{4}\times 2+\frac{1}{2}
Substitute 2 for x in the equation y=\frac{5}{4}x+\frac{1}{2}.
y=3
Calculate y from y=\frac{5}{4}\times 2+\frac{1}{2}.
z=2\times 2-3\times 3+4
Substitute 3 for y and 2 for x in the equation z=2x-3y+4.
z=-1
Calculate z from z=2\times 2-3\times 3+4.
x=2 y=3 z=-1
The system is now solved.
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