Solve 2/7y+20=1/17z+10

$$\frac { 2 } { 7 } y + 20 = \frac { 1 } { 17 } z + 10$$

Solve for y

$$y=\frac{7\left(z-170\right)}{34}$$

Steps for Solving Linear Equation

Subtract 20 from both sides.

$$\frac{2}{7}y=\frac{1}{17}z+10-20$$

Subtract 20 from 10 to get -10.

$$\frac{2}{7}y=\frac{1}{17}z-10$$

The equation is in standard form.

$$\frac{2}{7}y=\frac{z}{17}-10$$

Divide both sides of the equation by \frac{2}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{7}y}{\frac{2}{7}}=\frac{\frac{z}{17}-10}{\frac{2}{7}}$$

Dividing by \frac{2}{7} undoes the multiplication by \frac{2}{7}.

$$y=\frac{\frac{z}{17}-10}{\frac{2}{7}}$$

Divide \frac{z}{17}-10 by \frac{2}{7} by multiplying \frac{z}{17}-10 by the reciprocal of \frac{2}{7}.

$$y=\frac{7z}{34}-35$$

Solve for z

$$z=\frac{34\left(y+35\right)}{7}$$

Steps for Solving Linear Equation

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

$$\frac{1}{17}z+10=\frac{2}{7}y+20$$

Subtract 10 from both sides.

$$\frac{1}{17}z=\frac{2}{7}y+20-10$$

Subtract 10 from 20 to get 10.

$$\frac{1}{17}z=\frac{2}{7}y+10$$

The equation is in standard form.

$$\frac{1}{17}z=\frac{2y}{7}+10$$

Multiply both sides by 17.

$$\frac{\frac{1}{17}z}{\frac{1}{17}}=\frac{\frac{2y}{7}+10}{\frac{1}{17}}$$

Dividing by \frac{1}{17} undoes the multiplication by \frac{1}{17}.

$$z=\frac{\frac{2y}{7}+10}{\frac{1}{17}}$$

Divide \frac{2y}{7}+10 by \frac{1}{17} by multiplying \frac{2y}{7}+10 by the reciprocal of \frac{1}{17}.

$$z=\frac{34y}{7}+170$$