\left\{ \begin{array} { l } { 3 x + y + 2 x = 2 } \\ { 2 x + y + 3 z = 11 } \\ { x - y - 4 z = - 10 } \end{array} \right.
Solve for x, y, z
x=2
y=-8
z=5
Share
Copied to clipboard
y=-5x+2
Solve 3x+y+2x=2 for y.
2x-5x+2+3z=11 x-\left(-5x+2\right)-4z=-10
Substitute -5x+2 for y in the second and third equation.
x=-3+z z=2+\frac{3}{2}x
Solve these equations for x and z respectively.
z=2+\frac{3}{2}\left(-3+z\right)
Substitute -3+z for x in the equation z=2+\frac{3}{2}x.
z=5
Solve z=2+\frac{3}{2}\left(-3+z\right) for z.
x=-3+5
Substitute 5 for z in the equation x=-3+z.
x=2
Calculate x from x=-3+5.
y=-5\times 2+2
Substitute 2 for x in the equation y=-5x+2.
y=-8
Calculate y from y=-5\times 2+2.
x=2 y=-8 z=5
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}