Solve y=7x-9/3x-7

$$y = \frac { 7 x - 9 } { 3 x - 7 }$$

Solve for x

$$x=-\frac{9-7y}{3y-7}$$

$$y\neq \frac{7}{3}$$

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.

$$y\left(3x-7\right)=7x-9$$

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

$$3yx-7y=7x-9$$

Subtract 7x from both sides.

$$3yx-7y-7x=-9$$

Add 7y to both sides.

$$3yx-7x=-9+7y$$

Combine all terms containing x.

$$\left(3y-7\right)x=-9+7y$$

The equation is in standard form.

$$\left(3y-7\right)x=7y-9$$

Divide both sides by 3y-7.

$$\frac{\left(3y-7\right)x}{3y-7}=\frac{7y-9}{3y-7}$$

Dividing by 3y-7 undoes the multiplication by 3y-7.

$$x=\frac{7y-9}{3y-7}$$

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

$$x=\frac{7y-9}{3y-7}\text{, }x\neq \frac{7}{3}$$

Solve for y

$$y=-\frac{9-7x}{3x-7}$$

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