Solve for x, y, z
x=1
y=-1
z=1
Share
Copied to clipboard
x+2y+3z=2 3x+5y+6z=4 2x+4y+5z=3
Reorder the equations.
x=-2y-3z+2
Solve x+2y+3z=2 for x.
3\left(-2y-3z+2\right)+5y+6z=4 2\left(-2y-3z+2\right)+4y+5z=3
Substitute -2y-3z+2 for x in the second and third equation.
y=-3z+2 z=1
Solve these equations for y and z respectively.
y=-3+2
Substitute 1 for z in the equation y=-3z+2.
y=-1
Calculate y from y=-3+2.
x=-2\left(-1\right)-3+2
Substitute -1 for y and 1 for z in the equation x=-2y-3z+2.
x=1
Calculate x from x=-2\left(-1\right)-3+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}