Solve 6x-4y+5/y=3

$$\frac{ 6x-4y+5 }{ y } =3$$

Solve for x

$$x=\frac{7y-5}{6}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$6x-4y+5=3y$$

Add 4y to both sides.

$$6x+5=3y+4y$$

Combine 3y and 4y to get 7y.

$$6x+5=7y$$

Subtract 5 from both sides.

$$6x=7y-5$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{7y-5}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{7y-5}{6}$$

Solve for y

$$y=\frac{6x+5}{7}$$

$$x\neq -\frac{5}{6}$$

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 y.

$$6x-4y+5=3y$$

Subtract 3y from both sides.

$$6x-4y+5-3y=0$$

Combine -4y and -3y to get -7y.

$$6x-7y+5=0$$

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$-7y+5=-6x$$

Subtract 5 from both sides.

$$-7y=-6x-5$$

Divide both sides by -7.

$$\frac{-7y}{-7}=\frac{-6x-5}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$y=\frac{-6x-5}{-7}$$

Divide -6x-5 by -7.

$$y=\frac{6x+5}{7}$$

Variable y cannot be equal to 0.

$$y=\frac{6x+5}{7}\text{, }y\neq 0$$