Solve y=2x-7/3x+7

$$y = \frac { 2 x - 7 } { 3 x + 7 }$$

Solve for x

$$x=-\frac{7\left(y+1\right)}{3y-2}$$

$$y\neq \frac{2}{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{7}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+7.

$$y\left(3x+7\right)=2x-7$$

Use the distributive property to multiply y by 3x+7.

$$3yx+7y=2x-7$$

Subtract 2x from both sides.

$$3yx+7y-2x=-7$$

Subtract 7y from both sides.

$$3yx-2x=-7-7y$$

Combine all terms containing x.

$$\left(3y-2\right)x=-7-7y$$

The equation is in standard form.

$$\left(3y-2\right)x=-7y-7$$

Divide both sides by 3y-2.

$$\frac{\left(3y-2\right)x}{3y-2}=\frac{-7y-7}{3y-2}$$

Dividing by 3y-2 undoes the multiplication by 3y-2.

$$x=\frac{-7y-7}{3y-2}$$

Divide -7-7y by 3y-2.

$$x=-\frac{7\left(y+1\right)}{3y-2}$$

Variable x cannot be equal to -\frac{7}{3}.

$$x=-\frac{7\left(y+1\right)}{3y-2}\text{, }x\neq -\frac{7}{3}$$

Solve for y

$$y=-\frac{7-2x}{3x+7}$$

$$x\neq -\frac{7}{3}$$