Solve a/7y+20=1/17z+10

$$\frac { a } { 7 } y + 20 = \frac { 1 } { 17 } z + 10$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{7\left(170-z\right)}{17y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&z=170\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 119, the least common multiple of 7,17.

$$17ay+2380=7z+1190$$

Subtract 2380 from both sides.

$$17ay=7z+1190-2380$$

Subtract 2380 from 1190 to get -1190.

$$17ay=7z-1190$$

The equation is in standard form.

$$17ya=7z-1190$$

Divide both sides by 17y.

$$\frac{17ya}{17y}=\frac{7z-1190}{17y}$$

Dividing by 17y undoes the multiplication by 17y.

$$a=\frac{7z-1190}{17y}$$

Divide -1190+7z by 17y.

$$a=\frac{7\left(z-170\right)}{17y}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{7\left(170-z\right)}{17a}\text{, }&a\neq 0\\y\in \mathrm{R}\text{, }&z=170\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 119, the least common multiple of 7,17.

$$17ay+2380=7z+1190$$

Subtract 2380 from both sides.

$$17ay=7z+1190-2380$$

Subtract 2380 from 1190 to get -1190.

$$17ay=7z-1190$$

Divide both sides by 17a.

$$\frac{17ay}{17a}=\frac{7z-1190}{17a}$$

Dividing by 17a undoes the multiplication by 17a.

$$y=\frac{7z-1190}{17a}$$

Divide -1190+7z by 17a.

$$y=\frac{7\left(z-170\right)}{17a}$$