Solve y=1/200a-1/10b+8

$$y = \frac { 1 } { 200 } a - \frac { 1 } { 10 } b + 8$$

Solve for a

$$a=20\left(10y+b-80\right)$$

Steps for Solving Linear Equation

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

$$\frac{1}{200}a-\frac{1}{10}b+8=y$$

Add \frac{1}{10}b to both sides.

$$\frac{1}{200}a+8=y+\frac{1}{10}b$$

Subtract 8 from both sides.

$$\frac{1}{200}a=y+\frac{1}{10}b-8$$

The equation is in standard form.

$$\frac{1}{200}a=\frac{b}{10}+y-8$$

Multiply both sides by 200.

$$\frac{\frac{1}{200}a}{\frac{1}{200}}=\frac{\frac{b}{10}+y-8}{\frac{1}{200}}$$

Dividing by \frac{1}{200} undoes the multiplication by \frac{1}{200}.

$$a=\frac{\frac{b}{10}+y-8}{\frac{1}{200}}$$

Divide y+\frac{b}{10}-8 by \frac{1}{200} by multiplying y+\frac{b}{10}-8 by the reciprocal of \frac{1}{200}.

$$a=200y+20b-1600$$

Solve for b

$$b=\frac{1600+a-200y}{20}$$

Steps for Solving Linear Equation

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

$$\frac{1}{200}a-\frac{1}{10}b+8=y$$

Subtract \frac{1}{200}a from both sides.

$$-\frac{1}{10}b+8=y-\frac{1}{200}a$$

Subtract 8 from both sides.

$$-\frac{1}{10}b=y-\frac{1}{200}a-8$$

The equation is in standard form.

$$-\frac{1}{10}b=-\frac{a}{200}+y-8$$

Multiply both sides by -10.

$$\frac{-\frac{1}{10}b}{-\frac{1}{10}}=\frac{-\frac{a}{200}+y-8}{-\frac{1}{10}}$$

Dividing by -\frac{1}{10} undoes the multiplication by -\frac{1}{10}.

$$b=\frac{-\frac{a}{200}+y-8}{-\frac{1}{10}}$$

Divide y-\frac{a}{200}-8 by -\frac{1}{10} by multiplying y-\frac{a}{200}-8 by the reciprocal of -\frac{1}{10}.

$$b=\frac{a}{20}-10y+80$$