Solve for x, y, z
x=1
y=-2
z=3
Share
Copied to clipboard
x=-2y-3z+6
Solve x+2y+3z=6 for x.
2\left(-2y-3z+6\right)-3y+2z=14 3\left(-2y-3z+6\right)+y-z=-2
Substitute -2y-3z+6 for x in the second and third equation.
y=-\frac{2}{7}-\frac{4}{7}z z=2-\frac{1}{2}y
Solve these equations for y and z respectively.
z=2-\frac{1}{2}\left(-\frac{2}{7}-\frac{4}{7}z\right)
Substitute -\frac{2}{7}-\frac{4}{7}z for y in the equation z=2-\frac{1}{2}y.
z=3
Solve z=2-\frac{1}{2}\left(-\frac{2}{7}-\frac{4}{7}z\right) for z.
y=-\frac{2}{7}-\frac{4}{7}\times 3
Substitute 3 for z in the equation y=-\frac{2}{7}-\frac{4}{7}z.
y=-2
Calculate y from y=-\frac{2}{7}-\frac{4}{7}\times 3.
x=-2\left(-2\right)-3\times 3+6
Substitute -2 for y and 3 for z in the equation x=-2y-3z+6.
x=1
Calculate x from x=-2\left(-2\right)-3\times 3+6.
x=1 y=-2 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}