Solve r:x+y-4=0

$$r : x + y - 4 = 0$$

Solve for r

$$r=-x\left(y-4\right)$$

$$x\neq 0$$

Solution Steps

Multiply both sides of the equation by x.

$$r+xy+x\left(-4\right)=0$$

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

$$r+x\left(-4\right)=-xy$$

Subtract x\left(-4\right) from both sides.

$$r=-xy-x\left(-4\right)$$

Multiply -1 and -4 to get 4.

$$r=-xy+4x$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{r}{y-4}\text{, }&r\neq 0\text{ and }y\neq 4\\x\neq 0\text{, }&y=4\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$r+xy+x\left(-4\right)=0$$

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

$$xy+x\left(-4\right)=-r$$

Combine all terms containing x.

$$\left(y-4\right)x=-r$$

Divide both sides by y-4.

$$\frac{\left(y-4\right)x}{y-4}=-\frac{r}{y-4}$$

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

$$x=-\frac{r}{y-4}$$

Variable x cannot be equal to 0.

$$x=-\frac{r}{y-4}\text{, }x\neq 0$$