\left\{ \begin{array} { l } { x + y - z = 11 } \\ { - x + y + z = 5 } \\ { x - y + z = 1 } \end{array} \right.
Solve for x, y, z
x=6
y=8
z=3
Share
Copied to clipboard
x=-y+z+11
Solve x+y-z=11 for x.
-\left(-y+z+11\right)+y+z=5 -y+z+11-y+z=1
Substitute -y+z+11 for x in the second and third equation.
y=8 z=-5+y
Solve these equations for y and z respectively.
z=-5+8
Substitute 8 for y in the equation z=-5+y.
z=3
Calculate z from z=-5+8.
x=-8+3+11
Substitute 8 for y and 3 for z in the equation x=-y+z+11.
x=6
Calculate x from x=-8+3+11.
x=6 y=8 z=3
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}