\left\{ \begin{array} { l } { x - y + 2 z = 2 } \\ { 2 x + 2 y - z = 5 } \\ { 3 x + 2 y - z = 2 } \end{array} \right.
Solve for x, y, z
x=-3
y=9
z=7
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x=y-2z+2
Solve x-y+2z=2 for x.
2\left(y-2z+2\right)+2y-z=5 3\left(y-2z+2\right)+2y-z=2
Substitute y-2z+2 for x in the second and third equation.
y=\frac{5}{4}z+\frac{1}{4} z=\frac{5}{7}y+\frac{4}{7}
Solve these equations for y and z respectively.
z=\frac{5}{7}\left(\frac{5}{4}z+\frac{1}{4}\right)+\frac{4}{7}
Substitute \frac{5}{4}z+\frac{1}{4} for y in the equation z=\frac{5}{7}y+\frac{4}{7}.
z=7
Solve z=\frac{5}{7}\left(\frac{5}{4}z+\frac{1}{4}\right)+\frac{4}{7} for z.
y=\frac{5}{4}\times 7+\frac{1}{4}
Substitute 7 for z in the equation y=\frac{5}{4}z+\frac{1}{4}.
y=9
Calculate y from y=\frac{5}{4}\times 7+\frac{1}{4}.
x=9-2\times 7+2
Substitute 9 for y and 7 for z in the equation x=y-2z+2.
x=-3
Calculate x from x=9-2\times 7+2.
x=-3 y=9 z=7
The system is now solved.
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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