Solve y=mx+1/m+1

$$y = m x + \frac { 1 } { m + 1 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{1-y-my}{m\left(m+1\right)}\text{, }&m\neq -1\text{ and }m\neq 0\\x\in \mathrm{C}\text{, }&m=0\text{ and }y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m+1.

$$y\left(m+1\right)=mx\left(m+1\right)+1$$

Use the distributive property to multiply y by m+1.

$$ym+y=mx\left(m+1\right)+1$$

Use the distributive property to multiply mx by m+1.

$$ym+y=xm^{2}+mx+1$$

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

$$xm^{2}+mx+1=ym+y$$

Subtract 1 from both sides.

$$xm^{2}+mx=ym+y-1$$

Combine all terms containing x.

$$\left(m^{2}+m\right)x=ym+y-1$$

The equation is in standard form.

$$\left(m^{2}+m\right)x=my+y-1$$

Divide both sides by m^{2}+m.

$$\frac{\left(m^{2}+m\right)x}{m^{2}+m}=\frac{my+y-1}{m^{2}+m}$$

Dividing by m^{2}+m undoes the multiplication by m^{2}+m.

$$x=\frac{my+y-1}{m^{2}+m}$$

Divide ym+y-1 by m^{2}+m.

$$x=\frac{my+y-1}{m\left(m+1\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{1-y-my}{m\left(m+1\right)}\text{, }&m\neq -1\text{ and }m\neq 0\\x\in \mathrm{R}\text{, }&m=0\text{ and }y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m+1.

$$y\left(m+1\right)=mx\left(m+1\right)+1$$

Use the distributive property to multiply y by m+1.

$$ym+y=mx\left(m+1\right)+1$$

Use the distributive property to multiply mx by m+1.

$$ym+y=xm^{2}+mx+1$$

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

$$xm^{2}+mx+1=ym+y$$

Subtract 1 from both sides.

$$xm^{2}+mx=ym+y-1$$

Combine all terms containing x.

$$\left(m^{2}+m\right)x=ym+y-1$$

The equation is in standard form.

$$\left(m^{2}+m\right)x=my+y-1$$

Divide both sides by m^{2}+m.

$$\frac{\left(m^{2}+m\right)x}{m^{2}+m}=\frac{my+y-1}{m^{2}+m}$$

Dividing by m^{2}+m undoes the multiplication by m^{2}+m.

$$x=\frac{my+y-1}{m^{2}+m}$$

Divide ym+y-1 by m^{2}+m.

$$x=\frac{my+y-1}{m\left(m+1\right)}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{\sqrt{x^{2}+2xy-4x+y^{2}}+x-y}{2x}\text{; }m=-\frac{-\sqrt{x^{2}+2xy-4x+y^{2}}+x-y}{2x}\text{, }&x\neq 0\\m=\frac{1-y}{y}\text{, }&x=0\text{ and }y\neq 0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{\sqrt{x^{2}+2xy-4x+y^{2}}+x-y}{2x}\text{; }m=-\frac{-\sqrt{x^{2}+2xy-4x+y^{2}}+x-y}{2x}\text{, }&x\neq 0\text{ and }\left(y\geq -x+2\sqrt{x}\text{ or }y\leq -x-2\sqrt{x}\text{ or }x<0\right)\\m=\frac{1-y}{y}\text{, }&x=0\text{ and }y\neq 0\end{matrix}\right.$$