Solve y/11frac{2{3}}=y+z/20

$$\frac { y } { 11 \frac { 2 } { 3 } } = \frac { y + z } { 20 }$$

Solve for y

$$y=\frac{7z}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20.

$$\frac{12}{7}y=y+z$$

Subtract y from both sides.

$$\frac{12}{7}y-y=z$$

Combine \frac{12}{7}y and -y to get \frac{5}{7}y.

$$\frac{5}{7}y=z$$

Divide both sides of the equation by \frac{5}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{7}y}{\frac{5}{7}}=\frac{z}{\frac{5}{7}}$$

Dividing by \frac{5}{7} undoes the multiplication by \frac{5}{7}.

$$y=\frac{z}{\frac{5}{7}}$$

Divide z by \frac{5}{7} by multiplying z by the reciprocal of \frac{5}{7}.

$$y=\frac{7z}{5}$$

Solve for z

$$z=\frac{5y}{7}$$

Solution Steps

Multiply both sides of the equation by 20.

$$\frac{12}{7}y=y+z$$

Swap sides so that all variable terms are on the left hand side.

$$y+z=\frac{12}{7}y$$

Subtract y from both sides.

$$z=\frac{12}{7}y-y$$

Combine \frac{12}{7}y and -y to get \frac{5}{7}y.

$$z=\frac{5}{7}y$$