Solve for t (complex solution)
\left\{\begin{matrix}t=\frac{4x}{x+y}\text{, }&x\neq -y\\t\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{ty}{4-t}\text{, }&t\neq 4\\x\in \mathrm{C}\text{, }&y=0\text{ and }t=4\end{matrix}\right.
Solve for t
\left\{\begin{matrix}t=\frac{4x}{x+y}\text{, }&x\neq -y\\t\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{ty}{4-t}\text{, }&t\neq 4\\x\in \mathrm{R}\text{, }&y=0\text{ and }t=4\end{matrix}\right.
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4x=t\left(x+y\right)
Combine 2x and 2x to get 4x.
4x=tx+ty
Use the distributive property to multiply t by x+y.
tx+ty=4x
Swap sides so that all variable terms are on the left hand side.
\left(x+y\right)t=4x
Combine all terms containing t.
\frac{\left(x+y\right)t}{x+y}=\frac{4x}{x+y}
Divide both sides by x+y.
t=\frac{4x}{x+y}
Dividing by x+y undoes the multiplication by x+y.
4x=t\left(x+y\right)
Combine 2x and 2x to get 4x.
4x=tx+ty
Use the distributive property to multiply t by x+y.
4x-tx=ty
Subtract tx from both sides.
\left(4-t\right)x=ty
Combine all terms containing x.
\frac{\left(4-t\right)x}{4-t}=\frac{ty}{4-t}
Divide both sides by 4-t.
x=\frac{ty}{4-t}
Dividing by 4-t undoes the multiplication by 4-t.
4x=t\left(x+y\right)
Combine 2x and 2x to get 4x.
4x=tx+ty
Use the distributive property to multiply t by x+y.
tx+ty=4x
Swap sides so that all variable terms are on the left hand side.
\left(x+y\right)t=4x
Combine all terms containing t.
\frac{\left(x+y\right)t}{x+y}=\frac{4x}{x+y}
Divide both sides by x+y.
t=\frac{4x}{x+y}
Dividing by x+y undoes the multiplication by x+y.
4x=t\left(x+y\right)
Combine 2x and 2x to get 4x.
4x=tx+ty
Use the distributive property to multiply t by x+y.
4x-tx=ty
Subtract tx from both sides.
\left(4-t\right)x=ty
Combine all terms containing x.
\frac{\left(4-t\right)x}{4-t}=\frac{ty}{4-t}
Divide both sides by 4-t.
x=\frac{ty}{4-t}
Dividing by 4-t undoes the multiplication by 4-t.
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}