Solve for x

\left\{\begin{matrix}\\x=z\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.

Solve for y

\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=z\end{matrix}\right.

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xz+yz=zx+yx

Use the distributive property to multiply x+y by z.

xz+yz-zx=yx

Subtract zx from both sides.

yz=yx

Combine xz and -zx to get 0.

yx=yz

Swap sides so that all variable terms are on the left hand side.

\frac{yx}{y}=\frac{yz}{y}

Divide both sides by y.

x=\frac{yz}{y}

Dividing by y undoes the multiplication by y.

x=z

Divide yz by y.

xz+yz=zx+yx

Use the distributive property to multiply x+y by z.

xz+yz-yx=zx

Subtract yx from both sides.

yz-yx=zx-xz

Subtract xz from both sides.

yz-yx=0

Combine zx and -xz to get 0.

\left(z-x\right)y=0

Combine all terms containing y.

y=0

Divide 0 by -x+z.

## 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}