\left\{ \begin{array} { l } { x + y - 2 z = - 3 } \\ { 5 x - 2 y + 7 z = 22 } \\ { 2 x - 5 y + 4 z = 4 } \end{array} \right.
Solve for x, y, z
x=1
y=2
z=3
Share
Copied to clipboard
x=-y+2z-3
Solve x+y-2z=-3 for x.
5\left(-y+2z-3\right)-2y+7z=22 2\left(-y+2z-3\right)-5y+4z=4
Substitute -y+2z-3 for x in the second and third equation.
y=\frac{17}{7}z-\frac{37}{7} z=\frac{7}{8}y+\frac{5}{4}
Solve these equations for y and z respectively.
z=\frac{7}{8}\left(\frac{17}{7}z-\frac{37}{7}\right)+\frac{5}{4}
Substitute \frac{17}{7}z-\frac{37}{7} for y in the equation z=\frac{7}{8}y+\frac{5}{4}.
z=3
Solve z=\frac{7}{8}\left(\frac{17}{7}z-\frac{37}{7}\right)+\frac{5}{4} for z.
y=\frac{17}{7}\times 3-\frac{37}{7}
Substitute 3 for z in the equation y=\frac{17}{7}z-\frac{37}{7}.
y=2
Calculate y from y=\frac{17}{7}\times 3-\frac{37}{7}.
x=-2+2\times 3-3
Substitute 2 for y and 3 for z in the equation x=-y+2z-3.
x=1
Calculate x from x=-2+2\times 3-3.
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}