Solve y-10x-operatorname{prg}x=3

$$y - 10 x - \operatorname { prg } x = 3$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{-10x+y-3}{prx}\text{, }&x\neq 0\text{ and }r\neq 0\text{ and }p\neq 0\\g\in \mathrm{C}\text{, }&\left(y=10x+3\text{ and }p=0\right)\text{ or }\left(y=10x+3\text{ and }r=0\right)\text{ or }\left(y=3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$-10x-prgx=3-y$$

Add 10x to both sides.

$$-prgx=3-y+10x$$

The equation is in standard form.

$$\left(-prx\right)g=10x-y+3$$

Divide both sides by -prx.

$$\frac{\left(-prx\right)g}{-prx}=\frac{10x-y+3}{-prx}$$

Dividing by -prx undoes the multiplication by -prx.

$$g=\frac{10x-y+3}{-prx}$$

Divide -y+10x+3 by -prx.

$$g=-\frac{10x-y+3}{prx}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{-10x+y-3}{grx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }r\neq 0\\p\in \mathrm{C}\text{, }&\left(y=10x+3\text{ and }r=0\right)\text{ or }\left(y=10x+3\text{ and }g=0\right)\text{ or }\left(y=3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$-10x-prgx=3-y$$

Add 10x to both sides.

$$-prgx=3-y+10x$$

The equation is in standard form.

$$\left(-grx\right)p=10x-y+3$$

Divide both sides by -rgx.

$$\frac{\left(-grx\right)p}{-grx}=\frac{10x-y+3}{-grx}$$

Dividing by -rgx undoes the multiplication by -rgx.

$$p=\frac{10x-y+3}{-grx}$$

Divide -y+10x+3 by -rgx.

$$p=-\frac{10x-y+3}{grx}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{-10x+y-3}{prx}\text{, }&x\neq 0\text{ and }r\neq 0\text{ and }p\neq 0\\g\in \mathrm{R}\text{, }&\left(y=10x+3\text{ and }p=0\right)\text{ or }\left(y=10x+3\text{ and }r=0\right)\text{ or }\left(y=3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$-10x-prgx=3-y$$

Add 10x to both sides.

$$-prgx=3-y+10x$$

The equation is in standard form.

$$\left(-prx\right)g=10x-y+3$$

Divide both sides by -prx.

$$\frac{\left(-prx\right)g}{-prx}=\frac{10x-y+3}{-prx}$$

Dividing by -prx undoes the multiplication by -prx.

$$g=\frac{10x-y+3}{-prx}$$

Divide 3-y+10x by -prx.

$$g=-\frac{10x-y+3}{prx}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{-10x+y-3}{grx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }r\neq 0\\p\in \mathrm{R}\text{, }&\left(y=10x+3\text{ and }r=0\right)\text{ or }\left(y=10x+3\text{ and }g=0\right)\text{ or }\left(y=3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$-10x-prgx=3-y$$

Add 10x to both sides.

$$-prgx=3-y+10x$$

The equation is in standard form.

$$\left(-grx\right)p=10x-y+3$$

Divide both sides by -rgx.

$$\frac{\left(-grx\right)p}{-grx}=\frac{10x-y+3}{-grx}$$

Dividing by -rgx undoes the multiplication by -rgx.

$$p=\frac{10x-y+3}{-grx}$$

Divide 3-y+10x by -rgx.

$$p=-\frac{10x-y+3}{grx}$$