Solve 7x+y25x+10z=1000000

$$7x+y25x+10z=1000000$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{10\left(z-100000\right)}{y_{25}+7}\text{, }&y_{25}\neq -7\\x\in \mathrm{R}\text{, }&z=100000\text{ and }y_{25}=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 10z from both sides.

$$7x+y_{25}x=1000000-10z$$

Combine all terms containing x.

$$\left(7+y_{25}\right)x=1000000-10z$$

The equation is in standard form.

$$\left(y_{25}+7\right)x=1000000-10z$$

Divide both sides by 7+y_{25}.

$$\frac{\left(y_{25}+7\right)x}{y_{25}+7}=\frac{1000000-10z}{y_{25}+7}$$

Dividing by 7+y_{25} undoes the multiplication by 7+y_{25}.

$$x=\frac{1000000-10z}{y_{25}+7}$$

Divide 1000000-10z by 7+y_{25}.

$$x=\frac{10\left(100000-z\right)}{y_{25}+7}$$

Solve for y_25

$$\left\{\begin{matrix}y_{25}=-\frac{7x+10z-1000000}{x}\text{, }&x\neq 0\\y_{25}\in \mathrm{R}\text{, }&x=0\text{ and }z=100000\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7x from both sides.

$$y_{25}x+10z=1000000-7x$$

Subtract 10z from both sides.

$$y_{25}x=1000000-7x-10z$$

The equation is in standard form.

$$xy_{25}=1000000-10z-7x$$

Divide both sides by x.

$$\frac{xy_{25}}{x}=\frac{1000000-10z-7x}{x}$$

Dividing by x undoes the multiplication by x.

$$y_{25}=\frac{1000000-10z-7x}{x}$$