\left\{ \begin{array} { l } { 3 x + 2 y + z = 11 } \\ { 2 x + 3 y + 2 z = 11 } \\ { 4 x + 3 y + 3 z = 11 } \end{array} \right.
Solve for x, y, z
x = \frac{11}{7} = 1\frac{4}{7} \approx 1.571428571
y = \frac{33}{7} = 4\frac{5}{7} \approx 4.714285714
z = -\frac{22}{7} = -3\frac{1}{7} \approx -3.142857143
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z=-3x-2y+11
Solve 3x+2y+z=11 for z.
2x+3y+2\left(-3x-2y+11\right)=11 4x+3y+3\left(-3x-2y+11\right)=11
Substitute -3x-2y+11 for z in the second and third equation.
y=-4x+11 x=-\frac{3}{5}y+\frac{22}{5}
Solve these equations for y and x respectively.
x=-\frac{3}{5}\left(-4x+11\right)+\frac{22}{5}
Substitute -4x+11 for y in the equation x=-\frac{3}{5}y+\frac{22}{5}.
x=\frac{11}{7}
Solve x=-\frac{3}{5}\left(-4x+11\right)+\frac{22}{5} for x.
y=-4\times \frac{11}{7}+11
Substitute \frac{11}{7} for x in the equation y=-4x+11.
y=\frac{33}{7}
Calculate y from y=-4\times \frac{11}{7}+11.
z=-3\times \frac{11}{7}-2\times \frac{33}{7}+11
Substitute \frac{33}{7} for y and \frac{11}{7} for x in the equation z=-3x-2y+11.
z=-\frac{22}{7}
Calculate z from z=-3\times \frac{11}{7}-2\times \frac{33}{7}+11.
x=\frac{11}{7} y=\frac{33}{7} z=-\frac{22}{7}
The system is now solved.
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