Solve x+y/2=A/2*(x+y)

$$\frac { x + y } { 2 } = \frac { A } { 2 } \times ( x + y )$$

Solve for A (complex solution)

$$\left\{\begin{matrix}\\A=1\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&x=-y\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x+y=A\left(x+y\right)$$

Use the distributive property to multiply A by x+y.

$$x+y=Ax+Ay$$

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

$$Ax+Ay=x+y$$

Combine all terms containing A.

$$\left(x+y\right)A=x+y$$

Divide both sides by x+y.

$$\frac{\left(x+y\right)A}{x+y}=\frac{x+y}{x+y}$$

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

$$A=\frac{x+y}{x+y}$$

Divide x+y by x+y.

$$A=1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-y\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&A=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x+y=A\left(x+y\right)$$

Use the distributive property to multiply A by x+y.

$$x+y=Ax+Ay$$

Subtract Ax from both sides.

$$x+y-Ax=Ay$$

Subtract y from both sides.

$$x-Ax=Ay-y$$

Combine all terms containing x.

$$\left(1-A\right)x=Ay-y$$

Divide both sides by 1-A.

$$\frac{\left(1-A\right)x}{1-A}=\frac{y\left(A-1\right)}{1-A}$$

Dividing by 1-A undoes the multiplication by 1-A.

$$x=\frac{y\left(A-1\right)}{1-A}$$

Divide y\left(-1+A\right) by 1-A.

$$x=-y$$

Solve for A

$$\left\{\begin{matrix}\\A=1\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&x=-y\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x+y=A\left(x+y\right)$$

Use the distributive property to multiply A by x+y.

$$x+y=Ax+Ay$$

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

$$Ax+Ay=x+y$$

Combine all terms containing A.

$$\left(x+y\right)A=x+y$$

Divide both sides by x+y.

$$\frac{\left(x+y\right)A}{x+y}=\frac{x+y}{x+y}$$

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

$$A=\frac{x+y}{x+y}$$

Divide x+y by x+y.

$$A=1$$

Solve for x

$$\left\{\begin{matrix}\\x=-y\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&A=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x+y=A\left(x+y\right)$$

Use the distributive property to multiply A by x+y.

$$x+y=Ax+Ay$$

Subtract Ax from both sides.

$$x+y-Ax=Ay$$

Subtract y from both sides.

$$x-Ax=Ay-y$$

Combine all terms containing x.

$$\left(1-A\right)x=Ay-y$$

Divide both sides by 1-A.

$$\frac{\left(1-A\right)x}{1-A}=\frac{y\left(A-1\right)}{1-A}$$

Dividing by 1-A undoes the multiplication by 1-A.

$$x=\frac{y\left(A-1\right)}{1-A}$$

Divide y\left(-1+A\right) by 1-A.

$$x=-y$$