Solve r*4x+5y=-15

$$r \cdot 4 x + 5 y = - 15$$

Solve for r

$$\left\{\begin{matrix}r=-\frac{5\left(y+3\right)}{4x}\text{, }&x\neq 0\\r\in \mathrm{R}\text{, }&y=-3\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5y from both sides.

$$r\times 4x=-15-5y$$

The equation is in standard form.

$$4xr=-5y-15$$

Divide both sides by 4x.

$$\frac{4xr}{4x}=\frac{-5y-15}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$r=\frac{-5y-15}{4x}$$

Divide -15-5y by 4x.

$$r=-\frac{5\left(y+3\right)}{4x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{5\left(y+3\right)}{4r}\text{, }&r\neq 0\\x\in \mathrm{R}\text{, }&y=-3\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5y from both sides.

$$r\times 4x=-15-5y$$

The equation is in standard form.

$$4rx=-5y-15$$

Divide both sides by 4r.

$$\frac{4rx}{4r}=\frac{-5y-15}{4r}$$

Dividing by 4r undoes the multiplication by 4r.

$$x=\frac{-5y-15}{4r}$$

Divide -15-5y by 4r.

$$x=-\frac{5\left(y+3\right)}{4r}$$