Solve n(x+y)+1/2x-1=0

$$n ( x + y ) + \frac { 1 } { 2 } x - 1 = 0$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{x-2}{2\left(x+y\right)}\text{, }&x\neq -y\\n\in \mathrm{R}\text{, }&x=2\text{ and }y=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$nx+ny+\frac{1}{2}x-1=0$$

Subtract \frac{1}{2}x from both sides. Anything subtracted from zero gives its negation.

$$nx+ny-1=-\frac{1}{2}x$$

Add 1 to both sides.

$$nx+ny=-\frac{1}{2}x+1$$

Combine all terms containing n.

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

The equation is in standard form.

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

Divide both sides by x+y.

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

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

$$n=\frac{-\frac{x}{2}+1}{x+y}$$

Divide -\frac{x}{2}+1 by x+y.

$$n=\frac{2-x}{2\left(x+y\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2\left(ny-1\right)}{2n+1}\text{, }&n\neq -\frac{1}{2}\\x\in \mathrm{R}\text{, }&y=-2\text{ and }n=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$nx+ny+\frac{1}{2}x-1=0$$

Subtract ny from both sides. Anything subtracted from zero gives its negation.

$$nx+\frac{1}{2}x-1=-ny$$

Add 1 to both sides.

$$nx+\frac{1}{2}x=-ny+1$$

Combine all terms containing x.

$$\left(n+\frac{1}{2}\right)x=-ny+1$$

The equation is in standard form.

$$\left(n+\frac{1}{2}\right)x=1-ny$$

Divide both sides by n+\frac{1}{2}.

$$\frac{\left(n+\frac{1}{2}\right)x}{n+\frac{1}{2}}=\frac{1-ny}{n+\frac{1}{2}}$$

Dividing by n+\frac{1}{2} undoes the multiplication by n+\frac{1}{2}.

$$x=\frac{1-ny}{n+\frac{1}{2}}$$

Divide -ny+1 by n+\frac{1}{2}.

$$x=\frac{2\left(1-ny\right)}{2n+1}$$