\left\{ \begin{array} { l } { x + y + z = 10 } \\ { 2 x + 3 y + z = 17 } \\ { 3 x + 2 y - z = 8 } \end{array} \right.
Solve for x, y, z
x=3
y=2
z=5
Share
Copied to clipboard
x=-y-z+10
Solve x+y+z=10 for x.
2\left(-y-z+10\right)+3y+z=17 3\left(-y-z+10\right)+2y-z=8
Substitute -y-z+10 for x in the second and third equation.
y=z-3 z=-\frac{1}{4}y+\frac{11}{2}
Solve these equations for y and z respectively.
z=-\frac{1}{4}\left(z-3\right)+\frac{11}{2}
Substitute z-3 for y in the equation z=-\frac{1}{4}y+\frac{11}{2}.
z=5
Solve z=-\frac{1}{4}\left(z-3\right)+\frac{11}{2} for z.
y=5-3
Substitute 5 for z in the equation y=z-3.
y=2
Calculate y from y=5-3.
x=-2-5+10
Substitute 2 for y and 5 for z in the equation x=-y-z+10.
x=3
Calculate x from x=-2-5+10.
x=3 y=2 z=5
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}