\left\{ \begin{array} { l } { 7 x + 4 y - z = 10 } \\ { x - 4 y + z = - 2 } \\ { 2 x - y - z = 0 } \end{array} \right.
Solve for x, y, z
x=1
y=1
z=1
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z=7x+4y-10
Solve 7x+4y-z=10 for z.
x-4y+7x+4y-10=-2 2x-y-\left(7x+4y-10\right)=0
Substitute 7x+4y-10 for z in the second and third equation.
x=1 y=2-x
Solve these equations for x and y respectively.
y=2-1
Substitute 1 for x in the equation y=2-x.
y=1
Calculate y from y=2-1.
z=7\times 1+4\times 1-10
Substitute 1 for x and 1 for y in the equation z=7x+4y-10.
z=1
Calculate z from z=7\times 1+4\times 1-10.
x=1 y=1 z=1
The system is now solved.
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