Solve for x, y, z
x=-6
y=-3
z=6
Share
Copied to clipboard
x=-2y-3z+6
Solve x+2y+3z=6 for x.
2\left(-2y-3z+6\right)-3y+z=3 3\left(-2y-3z+6\right)-4y+2z=6
Substitute -2y-3z+6 for x in the second and third equation.
y=-\frac{5}{7}z+\frac{9}{7} z=\frac{12}{7}-\frac{10}{7}y
Solve these equations for y and z respectively.
z=\frac{12}{7}-\frac{10}{7}\left(-\frac{5}{7}z+\frac{9}{7}\right)
Substitute -\frac{5}{7}z+\frac{9}{7} for y in the equation z=\frac{12}{7}-\frac{10}{7}y.
z=6
Solve z=\frac{12}{7}-\frac{10}{7}\left(-\frac{5}{7}z+\frac{9}{7}\right) for z.
y=-\frac{5}{7}\times 6+\frac{9}{7}
Substitute 6 for z in the equation y=-\frac{5}{7}z+\frac{9}{7}.
y=-3
Calculate y from y=-\frac{5}{7}\times 6+\frac{9}{7}.
x=-2\left(-3\right)-3\times 6+6
Substitute -3 for y and 6 for z in the equation x=-2y-3z+6.
x=-6
Calculate x from x=-2\left(-3\right)-3\times 6+6.
x=-6 y=-3 z=6
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}