Solve for x, y, z
x=7
y=4
z=1
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x+3y-4z=15 3x-7y+5z=-2 x-2y-6z=-7
Reorder the equations.
x=-3y+4z+15
Solve x+3y-4z=15 for x.
3\left(-3y+4z+15\right)-7y+5z=-2 -3y+4z+15-2y-6z=-7
Substitute -3y+4z+15 for x in the second and third equation.
y=\frac{17}{16}z+\frac{47}{16} z=-\frac{5}{2}y+11
Solve these equations for y and z respectively.
z=-\frac{5}{2}\left(\frac{17}{16}z+\frac{47}{16}\right)+11
Substitute \frac{17}{16}z+\frac{47}{16} for y in the equation z=-\frac{5}{2}y+11.
z=1
Solve z=-\frac{5}{2}\left(\frac{17}{16}z+\frac{47}{16}\right)+11 for z.
y=\frac{17}{16}\times 1+\frac{47}{16}
Substitute 1 for z in the equation y=\frac{17}{16}z+\frac{47}{16}.
y=4
Calculate y from y=\frac{17}{16}\times 1+\frac{47}{16}.
x=-3\times 4+4\times 1+15
Substitute 4 for y and 1 for z in the equation x=-3y+4z+15.
x=7
Calculate x from x=-3\times 4+4\times 1+15.
x=7 y=4 z=1
The system is now solved.
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