Solve for x
x=-\frac{z}{2}-\frac{3y}{2}+3
Solve for y
y=-\frac{z}{3}-\frac{2x}{3}+2
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6-2x-3y=z
Swap sides so that all variable terms are on the left hand side.
-2x-3y=z-6
Subtract 6 from both sides.
-2x=z-6+3y
Add 3y to both sides.
-2x=3y+z-6
The equation is in standard form.
\frac{-2x}{-2}=\frac{3y+z-6}{-2}
Divide both sides by -2.
x=\frac{3y+z-6}{-2}
Dividing by -2 undoes the multiplication by -2.
x=-\frac{z}{2}-\frac{3y}{2}+3
Divide z-6+3y by -2.
6-2x-3y=z
Swap sides so that all variable terms are on the left hand side.
-2x-3y=z-6
Subtract 6 from both sides.
-3y=z-6+2x
Add 2x to both sides.
-3y=2x+z-6
The equation is in standard form.
\frac{-3y}{-3}=\frac{2x+z-6}{-3}
Divide both sides by -3.
y=\frac{2x+z-6}{-3}
Dividing by -3 undoes the multiplication by -3.
y=-\frac{z}{3}-\frac{2x}{3}+2
Divide z-6+2x by -3.
Examples
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{ 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}