Solve x(m+2)+y(m-7)=2(m-3)

$$x ( m + 2 ) + y ( m - 7 ) = 2 ( m - 3 )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{2x-7y+6}{x+y-2}\text{, }&x\neq 2-y\\m\in \mathrm{C}\text{, }&x=\frac{8}{9}\text{ and }y=\frac{10}{9}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by m+2.

$$xm+2x+y\left(m-7\right)=2\left(m-3\right)$$

Use the distributive property to multiply y by m-7.

$$xm+2x+ym-7y=2\left(m-3\right)$$

Use the distributive property to multiply 2 by m-3.

$$xm+2x+ym-7y=2m-6$$

Subtract 2m from both sides.

$$xm+2x+ym-7y-2m=-6$$

Subtract 2x from both sides.

$$xm+ym-7y-2m=-6-2x$$

Add 7y to both sides.

$$xm+ym-2m=-6-2x+7y$$

Combine all terms containing m.

$$\left(x+y-2\right)m=-6-2x+7y$$

The equation is in standard form.

$$\left(x+y-2\right)m=-2x+7y-6$$

Divide both sides by x+y-2.

$$\frac{\left(x+y-2\right)m}{x+y-2}=\frac{-2x+7y-6}{x+y-2}$$

Dividing by x+y-2 undoes the multiplication by x+y-2.

$$m=\frac{-2x+7y-6}{x+y-2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{my-7y-2m+6}{m+2}\text{, }&m\neq -2\\x\in \mathrm{C}\text{, }&y=\frac{10}{9}\text{ and }m=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by m+2.

$$xm+2x+y\left(m-7\right)=2\left(m-3\right)$$

Use the distributive property to multiply y by m-7.

$$xm+2x+ym-7y=2\left(m-3\right)$$

Use the distributive property to multiply 2 by m-3.

$$xm+2x+ym-7y=2m-6$$

Subtract ym from both sides.

$$xm+2x-7y=2m-6-ym$$

Add 7y to both sides.

$$xm+2x=2m-6-ym+7y$$

Combine all terms containing x.

$$\left(m+2\right)x=2m-6-ym+7y$$

The equation is in standard form.

$$\left(m+2\right)x=-my+7y+2m-6$$

Divide both sides by m+2.

$$\frac{\left(m+2\right)x}{m+2}=\frac{-my+7y+2m-6}{m+2}$$

Dividing by m+2 undoes the multiplication by m+2.

$$x=\frac{-my+7y+2m-6}{m+2}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{2x-7y+6}{x+y-2}\text{, }&x\neq 2-y\\m\in \mathrm{R}\text{, }&x=\frac{8}{9}\text{ and }y=\frac{10}{9}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by m+2.

$$xm+2x+y\left(m-7\right)=2\left(m-3\right)$$

Use the distributive property to multiply y by m-7.

$$xm+2x+ym-7y=2\left(m-3\right)$$

Use the distributive property to multiply 2 by m-3.

$$xm+2x+ym-7y=2m-6$$

Subtract 2m from both sides.

$$xm+2x+ym-7y-2m=-6$$

Subtract 2x from both sides.

$$xm+ym-7y-2m=-6-2x$$

Add 7y to both sides.

$$xm+ym-2m=-6-2x+7y$$

Combine all terms containing m.

$$\left(x+y-2\right)m=-6-2x+7y$$

The equation is in standard form.

$$\left(x+y-2\right)m=-2x+7y-6$$

Divide both sides by x+y-2.

$$\frac{\left(x+y-2\right)m}{x+y-2}=\frac{-2x+7y-6}{x+y-2}$$

Dividing by x+y-2 undoes the multiplication by x+y-2.

$$m=\frac{-2x+7y-6}{x+y-2}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{my-7y-2m+6}{m+2}\text{, }&m\neq -2\\x\in \mathrm{R}\text{, }&y=\frac{10}{9}\text{ and }m=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by m+2.

$$xm+2x+y\left(m-7\right)=2\left(m-3\right)$$

Use the distributive property to multiply y by m-7.

$$xm+2x+ym-7y=2\left(m-3\right)$$

Use the distributive property to multiply 2 by m-3.

$$xm+2x+ym-7y=2m-6$$

Subtract ym from both sides.

$$xm+2x-7y=2m-6-ym$$

Add 7y to both sides.

$$xm+2x=2m-6-ym+7y$$

Combine all terms containing x.

$$\left(m+2\right)x=2m-6-ym+7y$$

The equation is in standard form.

$$\left(m+2\right)x=-my+7y+2m-6$$

Divide both sides by m+2.

$$\frac{\left(m+2\right)x}{m+2}=\frac{-my+7y+2m-6}{m+2}$$

Dividing by m+2 undoes the multiplication by m+2.

$$x=\frac{-my+7y+2m-6}{m+2}$$