Solve y-5/b=4/7

$$y - \frac { 5 } { b } = \frac { 4 } { 7 }$$

Solve for b

$$b=-\frac{35}{4-7y}$$

$$y\neq \frac{4}{7}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7b, the least common multiple of b,7.

$$7by-7\times 5=4b$$

Multiply -7 and 5 to get -35.

$$7by-35=4b$$

Subtract 4b from both sides.

$$7by-35-4b=0$$

Add 35 to both sides. Anything plus zero gives itself.

$$7by-4b=35$$

Combine all terms containing b.

$$\left(7y-4\right)b=35$$

Divide both sides by 7y-4.

$$\frac{\left(7y-4\right)b}{7y-4}=\frac{35}{7y-4}$$

Dividing by 7y-4 undoes the multiplication by 7y-4.

$$b=\frac{35}{7y-4}$$

Variable b cannot be equal to 0.

$$b=\frac{35}{7y-4}\text{, }b\neq 0$$

Solve for y

$$y=\frac{4}{7}+\frac{5}{b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

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

$$7by-7\times 5=4b$$

Multiply -7 and 5 to get -35.

$$7by-35=4b$$

Add 35 to both sides.

$$7by=4b+35$$

Divide both sides by 7b.

$$\frac{7by}{7b}=\frac{4b+35}{7b}$$

Dividing by 7b undoes the multiplication by 7b.

$$y=\frac{4b+35}{7b}$$

Divide 4b+35 by 7b.

$$y=\frac{4}{7}+\frac{5}{b}$$