\left\{ \begin{array} { l } { 4 x + y = 20 } \\ { x - 2 y = - 13 } \\ { y + z = 12 } \end{array} \right.
Solve for x, y, z
x=3
y=8
z=4
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y=20-4x
Solve 4x+y=20 for y.
x-2\left(20-4x\right)=-13 20-4x+z=12
Substitute 20-4x for y in the second and third equation.
x=3 z=-8+4x
Solve these equations for x and z respectively.
z=-8+4\times 3
Substitute 3 for x in the equation z=-8+4x.
z=4
Calculate z from z=-8+4\times 3.
y=20-4\times 3
Substitute 3 for x in the equation y=20-4x.
y=8
Calculate y from y=20-4\times 3.
x=3 y=8 z=4
The system is now solved.
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