Solve y=5-6x/2x+3

$$y = \frac{ 5-6x }{ 2x+3 }$$

Solve for x

$$x=-\frac{3y-5}{2\left(y+3\right)}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+3.

$$y\left(2x+3\right)=5-6x$$

Use the distributive property to multiply y by 2x+3.

$$2yx+3y=5-6x$$

Add 6x to both sides.

$$2yx+3y+6x=5$$

Subtract 3y from both sides.

$$2yx+6x=5-3y$$

Combine all terms containing x.

$$\left(2y+6\right)x=5-3y$$

Divide both sides by 2y+6.

$$\frac{\left(2y+6\right)x}{2y+6}=\frac{5-3y}{2y+6}$$

Dividing by 2y+6 undoes the multiplication by 2y+6.

$$x=\frac{5-3y}{2y+6}$$

Divide 5-3y by 2y+6.

$$x=\frac{5-3y}{2\left(y+3\right)}$$

Variable x cannot be equal to -\frac{3}{2}.

$$x=\frac{5-3y}{2\left(y+3\right)}\text{, }x\neq -\frac{3}{2}$$

Solve for y

$$y=-\frac{6x-5}{2x+3}$$

$$x\neq -\frac{3}{2}$$