\left\{ \begin{array} { l } { 2 x + y - z = 2 } \\ { 3 x + 2 y + 4 z = 9 } \\ { 5 x + 4 y + 2 z = 11 } \end{array} \right.
Solve for x, y, z
x=1
y=1
z=1
Share
Copied to clipboard
y=-2x+z+2
Solve 2x+y-z=2 for y.
3x+2\left(-2x+z+2\right)+4z=9 5x+4\left(-2x+z+2\right)+2z=11
Substitute -2x+z+2 for y in the second and third equation.
x=6z-5 z=\frac{1}{2}+\frac{1}{2}x
Solve these equations for x and z respectively.
z=\frac{1}{2}+\frac{1}{2}\left(6z-5\right)
Substitute 6z-5 for x in the equation z=\frac{1}{2}+\frac{1}{2}x.
z=1
Solve z=\frac{1}{2}+\frac{1}{2}\left(6z-5\right) for z.
x=6\times 1-5
Substitute 1 for z in the equation x=6z-5.
x=1
Calculate x from x=6\times 1-5.
y=-2+1+2
Substitute 1 for x and 1 for z in the equation y=-2x+z+2.
y=1
Calculate y from y=-2+1+2.
x=1 y=1 z=1
The system is now solved.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}