Solve 7x+3/5x-1=y

$$\frac { 7 x + 3 } { 5 x - 1 } = y$$

Solve for x

$$x=-\frac{y+3}{7-5y}$$

$$y\neq \frac{7}{5}$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 5x-1.

$$7x+3=y\left(5x-1\right)$$

Use the distributive property to multiply y by 5x-1.

$$7x+3=5yx-y$$

Subtract 5yx from both sides.

$$7x+3-5yx=-y$$

Subtract 3 from both sides.

$$7x-5yx=-y-3$$

Combine all terms containing x.

$$\left(7-5y\right)x=-y-3$$

Divide both sides by -5y+7.

$$\frac{\left(7-5y\right)x}{7-5y}=\frac{-y-3}{7-5y}$$

Dividing by -5y+7 undoes the multiplication by -5y+7.

$$x=\frac{-y-3}{7-5y}$$

Divide -y-3 by -5y+7.

$$x=-\frac{y+3}{7-5y}$$

Variable x cannot be equal to \frac{1}{5}.

$$x=-\frac{y+3}{7-5y}\text{, }x\neq \frac{1}{5}$$

Solve for y

$$y=-\frac{7x+3}{1-5x}$$

$$x\neq \frac{1}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5x-1.

$$7x+3=y\left(5x-1\right)$$

Use the distributive property to multiply y by 5x-1.

$$7x+3=5yx-y$$

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

$$5yx-y=7x+3$$

Combine all terms containing y.

$$\left(5x-1\right)y=7x+3$$

Divide both sides by 5x-1.

$$\frac{\left(5x-1\right)y}{5x-1}=\frac{7x+3}{5x-1}$$

Dividing by 5x-1 undoes the multiplication by 5x-1.

$$y=\frac{7x+3}{5x-1}$$