Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y+5z-6}{z}\text{, }&z\neq 0\\x\in \mathrm{C}\text{, }&y=6\text{ and }z=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y+5z-6}{z}\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=6\text{ and }z=0\end{matrix}\right.
Solve for y
y=xz-5z+6
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y-6=zx-5z
Use the distributive property to multiply z by x-5.
zx-5z=y-6
Swap sides so that all variable terms are on the left hand side.
zx=y-6+5z
Add 5z to both sides.
zx=y+5z-6
The equation is in standard form.
\frac{zx}{z}=\frac{y+5z-6}{z}
Divide both sides by z.
x=\frac{y+5z-6}{z}
Dividing by z undoes the multiplication by z.
y-6=zx-5z
Use the distributive property to multiply z by x-5.
zx-5z=y-6
Swap sides so that all variable terms are on the left hand side.
zx=y-6+5z
Add 5z to both sides.
zx=y+5z-6
The equation is in standard form.
\frac{zx}{z}=\frac{y+5z-6}{z}
Divide both sides by z.
x=\frac{y+5z-6}{z}
Dividing by z undoes the multiplication by z.
y-6=zx-5z
Use the distributive property to multiply z by x-5.
y=zx-5z+6
Add 6 to both sides.
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}