Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{5x+y+2}{3x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&y=-2\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y+2}{3m-5}\text{, }&m\neq \frac{5}{3}\\x\in \mathrm{C}\text{, }&y=-2\text{ and }m=\frac{5}{3}\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=\frac{5x+y+2}{3x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&y=-2\text{ and }x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y+2}{3m-5}\text{, }&m\neq \frac{5}{3}\\x\in \mathrm{R}\text{, }&y=-2\text{ and }m=\frac{5}{3}\end{matrix}\right.
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y=3mx-5x-2
Use the distributive property to multiply 3m-5 by x.
3mx-5x-2=y
Swap sides so that all variable terms are on the left hand side.
3mx-2=y+5x
Add 5x to both sides.
3mx=y+5x+2
Add 2 to both sides.
3xm=5x+y+2
The equation is in standard form.
\frac{3xm}{3x}=\frac{5x+y+2}{3x}
Divide both sides by 3x.
m=\frac{5x+y+2}{3x}
Dividing by 3x undoes the multiplication by 3x.
y=3mx-5x-2
Use the distributive property to multiply 3m-5 by x.
3mx-5x-2=y
Swap sides so that all variable terms are on the left hand side.
3mx-5x=y+2
Add 2 to both sides.
\left(3m-5\right)x=y+2
Combine all terms containing x.
\frac{\left(3m-5\right)x}{3m-5}=\frac{y+2}{3m-5}
Divide both sides by 3m-5.
x=\frac{y+2}{3m-5}
Dividing by 3m-5 undoes the multiplication by 3m-5.
y=3mx-5x-2
Use the distributive property to multiply 3m-5 by x.
3mx-5x-2=y
Swap sides so that all variable terms are on the left hand side.
3mx-2=y+5x
Add 5x to both sides.
3mx=y+5x+2
Add 2 to both sides.
3xm=5x+y+2
The equation is in standard form.
\frac{3xm}{3x}=\frac{5x+y+2}{3x}
Divide both sides by 3x.
m=\frac{5x+y+2}{3x}
Dividing by 3x undoes the multiplication by 3x.
y=3mx-5x-2
Use the distributive property to multiply 3m-5 by x.
3mx-5x-2=y
Swap sides so that all variable terms are on the left hand side.
3mx-5x=y+2
Add 2 to both sides.
\left(3m-5\right)x=y+2
Combine all terms containing x.
\frac{\left(3m-5\right)x}{3m-5}=\frac{y+2}{3m-5}
Divide both sides by 3m-5.
x=\frac{y+2}{3m-5}
Dividing by 3m-5 undoes the multiplication by 3m-5.
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}