Solve operatorname{ph}5x+3y=15

$$\operatorname { ph } 5 x + 3 y = 15$$

Solve for h_5 (complex solution)

$$\left\{\begin{matrix}h_{5}=-\frac{3\left(y-5\right)}{px}\text{, }&x\neq 0\text{ and }p\neq 0\\h_{5}\in \mathrm{C}\text{, }&\left(x=0\text{ or }p=0\right)\text{ and }y=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$ph_{5}x=15-3y$$

The equation is in standard form.

$$pxh_{5}=15-3y$$

Divide both sides by px.

$$\frac{pxh_{5}}{px}=\frac{15-3y}{px}$$

Dividing by px undoes the multiplication by px.

$$h_{5}=\frac{15-3y}{px}$$

Divide 15-3y by px.

$$h_{5}=\frac{3\left(5-y\right)}{px}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{3\left(y-5\right)}{h_{5}x}\text{, }&x\neq 0\text{ and }h_{5}\neq 0\\p\in \mathrm{C}\text{, }&\left(x=0\text{ or }h_{5}=0\right)\text{ and }y=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$ph_{5}x=15-3y$$

The equation is in standard form.

$$h_{5}xp=15-3y$$

Divide both sides by h_{5}x.

$$\frac{h_{5}xp}{h_{5}x}=\frac{15-3y}{h_{5}x}$$

Dividing by h_{5}x undoes the multiplication by h_{5}x.

$$p=\frac{15-3y}{h_{5}x}$$

Divide 15-3y by h_{5}x.

$$p=\frac{3\left(5-y\right)}{h_{5}x}$$

Solve for h_5

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

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$ph_{5}x=15-3y$$

The equation is in standard form.

$$pxh_{5}=15-3y$$

Divide both sides by px.

$$\frac{pxh_{5}}{px}=\frac{15-3y}{px}$$

Dividing by px undoes the multiplication by px.

$$h_{5}=\frac{15-3y}{px}$$

Divide 15-3y by px.

$$h_{5}=\frac{3\left(5-y\right)}{px}$$

Solve for p

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

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$ph_{5}x=15-3y$$

The equation is in standard form.

$$h_{5}xp=15-3y$$

Divide both sides by h_{5}x.

$$\frac{h_{5}xp}{h_{5}x}=\frac{15-3y}{h_{5}x}$$

Dividing by h_{5}x undoes the multiplication by h_{5}x.

$$p=\frac{15-3y}{h_{5}x}$$

Divide 15-3y by h_{5}x.

$$p=\frac{3\left(5-y\right)}{h_{5}x}$$