Solve for x, y, z
x=1
y=2
z=3
Share
Copied to clipboard
y=-2x+z+1
Solve 2x+y-z=1 for y.
3x+2\left(-2x+z+1\right)+z=10 2x-\left(-2x+z+1\right)+2z=6
Substitute -2x+z+1 for y in the second and third equation.
x=3z-8 z=-4x+7
Solve these equations for x and z respectively.
z=-4\left(3z-8\right)+7
Substitute 3z-8 for x in the equation z=-4x+7.
z=3
Solve z=-4\left(3z-8\right)+7 for z.
x=3\times 3-8
Substitute 3 for z in the equation x=3z-8.
x=1
Calculate x from x=3\times 3-8.
y=-2+3+1
Substitute 1 for x and 3 for z in the equation y=-2x+z+1.
y=2
Calculate y from y=-2+3+1.
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}