\left\{ \begin{array} { l } { 2 x - y + z = 6 } \\ { 3 x + 2 y - z = 5 } \\ { x - 3 y + 2 z = 5 } \end{array} \right.
Solve for x, y, z
x=2
y=1
z=3
Share
Copied to clipboard
y=2x+z-6
Solve 2x-y+z=6 for y.
3x+2\left(2x+z-6\right)-z=5 x-3\left(2x+z-6\right)+2z=5
Substitute 2x+z-6 for y in the second and third equation.
x=-\frac{1}{7}z+\frac{17}{7} z=-5x+13
Solve these equations for x and z respectively.
z=-5\left(-\frac{1}{7}z+\frac{17}{7}\right)+13
Substitute -\frac{1}{7}z+\frac{17}{7} for x in the equation z=-5x+13.
z=3
Solve z=-5\left(-\frac{1}{7}z+\frac{17}{7}\right)+13 for z.
x=-\frac{1}{7}\times 3+\frac{17}{7}
Substitute 3 for z in the equation x=-\frac{1}{7}z+\frac{17}{7}.
x=2
Calculate x from x=-\frac{1}{7}\times 3+\frac{17}{7}.
y=2\times 2+3-6
Substitute 2 for x and 3 for z in the equation y=2x+z-6.
y=1
Calculate y from y=2\times 2+3-6.
x=2 y=1 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}