Solve y=2x+7/3x+9

$$y = \frac { 2 x + 7 } { 3 x + 9 }$$

Solve for x

$$x=-\frac{9y-7}{3y-2}$$

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

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+3\right).

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

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

$$3yx+3y\times 3=2x+7$$

Multiply 3 and 3 to get 9.

$$3yx+9y=2x+7$$

Subtract 2x from both sides.

$$3yx+9y-2x=7$$

Subtract 9y from both sides.

$$3yx-2x=7-9y$$

Combine all terms containing x.

$$\left(3y-2\right)x=7-9y$$

Divide both sides by 3y-2.

$$\frac{\left(3y-2\right)x}{3y-2}=\frac{7-9y}{3y-2}$$

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

$$x=\frac{7-9y}{3y-2}$$

Variable x cannot be equal to -3.

$$x=\frac{7-9y}{3y-2}\text{, }x\neq -3$$

Solve for y

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

$$x\neq -3$$