Solve 2x+2x=b(x+y)

$$2 x + 2 x = b ( x + y )$$

Solve for b

$$\left\{\begin{matrix}b=\frac{4x}{x+y}\text{, }&x\neq -y\\b\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2x and 2x to get 4x.

$$4x=b\left(x+y\right)$$

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

$$4x=bx+by$$

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

$$bx+by=4x$$

Combine all terms containing b.

$$\left(x+y\right)b=4x$$

Divide both sides by x+y.

$$\frac{\left(x+y\right)b}{x+y}=\frac{4x}{x+y}$$

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

$$b=\frac{4x}{x+y}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{by}{4-b}\text{, }&b\neq 4\\x\in \mathrm{R}\text{, }&y=0\text{ and }b=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2x and 2x to get 4x.

$$4x=b\left(x+y\right)$$

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

$$4x=bx+by$$

Subtract bx from both sides.

$$4x-bx=by$$

Combine all terms containing x.

$$\left(4-b\right)x=by$$

Divide both sides by 4-b.

$$\frac{\left(4-b\right)x}{4-b}=\frac{by}{4-b}$$

Dividing by 4-b undoes the multiplication by 4-b.

$$x=\frac{by}{4-b}$$