Solve for x
x=\frac{3\left(y-3z+2\right)}{2}
Solve for y
y=\frac{2x}{3}+3z-2
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2x+9z-6=3y
Add 3y to both sides. Anything plus zero gives itself.
2x-6=3y-9z
Subtract 9z from both sides.
2x=3y-9z+6
Add 6 to both sides.
\frac{2x}{2}=\frac{3y-9z+6}{2}
Divide both sides by 2.
x=\frac{3y-9z+6}{2}
Dividing by 2 undoes the multiplication by 2.
x=\frac{3y}{2}-\frac{9z}{2}+3
Divide 6+3y-9z by 2.
-3y+9z-6=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
-3y-6=-2x-9z
Subtract 9z from both sides.
-3y=-2x-9z+6
Add 6 to both sides.
-3y=6-9z-2x
The equation is in standard form.
\frac{-3y}{-3}=\frac{6-9z-2x}{-3}
Divide both sides by -3.
y=\frac{6-9z-2x}{-3}
Dividing by -3 undoes the multiplication by -3.
y=\frac{2x}{3}+3z-2
Divide -2x-9z+6 by -3.
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}