Solve for x, y, z
x=5
y=0
z=0
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x=-y-z+5
Solve x+y+z=5 for x.
2\left(-y-z+5\right)+3y+5z=10 3\left(-y-z+5\right)+5y+7z=15
Substitute -y-z+5 for x in the second and third equation.
y=-3z z=-\frac{1}{2}y
Solve these equations for y and z respectively.
z=-\frac{1}{2}\left(-3\right)z
Substitute -3z for y in the equation z=-\frac{1}{2}y.
z=0
Solve z=-\frac{1}{2}\left(-3\right)z for z.
y=-3\times 0
Substitute 0 for z in the equation y=-3z.
y=0
Calculate y from y=-3\times 0.
x=-0-0+5
Substitute 0 for y and 0 for z in the equation x=-y-z+5.
x=5
Calculate x from x=-0-0+5.
x=5 y=0 z=0
The system is now solved.
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