Solve mx+7y=6x+15

$$m x + 7 y = 6 x + 15$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{-6x+7y-15}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }y=\frac{15}{7}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7y from both sides.

$$mx=6x+15-7y$$

The equation is in standard form.

$$xm=6x-7y+15$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{6x-7y+15}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{6x-7y+15}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{7y-15}{m-6}\text{, }&m\neq 6\\x\in \mathrm{C}\text{, }&y=\frac{15}{7}\text{ and }m=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6x from both sides.

$$mx+7y-6x=15$$

Subtract 7y from both sides.

$$mx-6x=15-7y$$

Combine all terms containing x.

$$\left(m-6\right)x=15-7y$$

Divide both sides by m-6.

$$\frac{\left(m-6\right)x}{m-6}=\frac{15-7y}{m-6}$$

Dividing by m-6 undoes the multiplication by m-6.

$$x=\frac{15-7y}{m-6}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{-6x+7y-15}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }y=\frac{15}{7}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7y from both sides.

$$mx=6x+15-7y$$

The equation is in standard form.

$$xm=6x-7y+15$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{6x-7y+15}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{6x-7y+15}{x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{7y-15}{m-6}\text{, }&m\neq 6\\x\in \mathrm{R}\text{, }&y=\frac{15}{7}\text{ and }m=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6x from both sides.

$$mx+7y-6x=15$$

Subtract 7y from both sides.

$$mx-6x=15-7y$$

Combine all terms containing x.

$$\left(m-6\right)x=15-7y$$

Divide both sides by m-6.

$$\frac{\left(m-6\right)x}{m-6}=\frac{15-7y}{m-6}$$

Dividing by m-6 undoes the multiplication by m-6.

$$x=\frac{15-7y}{m-6}$$