Solve 7/9+a/y=3

$$\frac { 7 } { 9 } + \frac { a } { y } = 3$$

Solve for a

$$a=\frac{20y}{9}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9y, the least common multiple of 9,y.

$$9y\times \frac{7}{9}+9a=27y$$

Multiply 9 and \frac{7}{9} to get 7.

$$7y+9a=27y$$

Subtract 7y from both sides.

$$9a=27y-7y$$

Combine 27y and -7y to get 20y.

$$9a=20y$$

Divide both sides by 9.

$$\frac{9a}{9}=\frac{20y}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$a=\frac{20y}{9}$$

Solve for y

$$y=\frac{9a}{20}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9y, the least common multiple of 9,y.

$$9y\times \frac{7}{9}+9a=27y$$

Multiply 9 and \frac{7}{9} to get 7.

$$7y+9a=27y$$

Subtract 27y from both sides.

$$7y+9a-27y=0$$

Combine 7y and -27y to get -20y.

$$-20y+9a=0$$

Subtract 9a from both sides. Anything subtracted from zero gives its negation.

$$-20y=-9a$$

Divide both sides by -20.

$$\frac{-20y}{-20}=-\frac{9a}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$y=-\frac{9a}{-20}$$

Divide -9a by -20.

$$y=\frac{9a}{20}$$

Variable y cannot be equal to 0.

$$y=\frac{9a}{20}\text{, }y\neq 0$$