Solve for x
x=\frac{-2y-z}{3}
Solve for y
y=\frac{-3x-z}{2}
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3x+2y+z=0
Swap sides so that all variable terms are on the left hand side.
3x+z=-2y
Subtract 2y from both sides. Anything subtracted from zero gives its negation.
3x=-2y-z
Subtract z from both sides.
\frac{3x}{3}=\frac{-2y-z}{3}
Divide both sides by 3.
x=\frac{-2y-z}{3}
Dividing by 3 undoes the multiplication by 3.
3x+2y+z=0
Swap sides so that all variable terms are on the left hand side.
2y+z=-3x
Subtract 3x from both sides. Anything subtracted from zero gives its negation.
2y=-3x-z
Subtract z from both sides.
\frac{2y}{2}=\frac{-3x-z}{2}
Divide both sides by 2.
y=\frac{-3x-z}{2}
Dividing by 2 undoes the multiplication by 2.
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}