\left\{ \begin{array} { l } { x + y + z = 1000 } \\ { 2 x + y + 4 z = 2000 } \\ { 2 x + 3 y + 5 z = 2500 } \end{array} \right.
Solve for x, y, z
x=700
y=200
z=100
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x=-y-z+1000
Solve x+y+z=1000 for x.
2\left(-y-z+1000\right)+y+4z=2000 2\left(-y-z+1000\right)+3y+5z=2500
Substitute -y-z+1000 for x in the second and third equation.
y=2z z=-\frac{1}{3}y+\frac{500}{3}
Solve these equations for y and z respectively.
z=-\frac{1}{3}\times 2z+\frac{500}{3}
Substitute 2z for y in the equation z=-\frac{1}{3}y+\frac{500}{3}.
z=100
Solve z=-\frac{1}{3}\times 2z+\frac{500}{3} for z.
y=2\times 100
Substitute 100 for z in the equation y=2z.
y=200
Calculate y from y=2\times 100.
x=-200-100+1000
Substitute 200 for y and 100 for z in the equation x=-y-z+1000.
x=700
Calculate x from x=-200-100+1000.
x=700 y=200 z=100
The system is now solved.
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