Solve y=-5x+2/9x+5

$$y = \frac { - 5 x + 2 } { 9 x + 5 }$$

Solve for x

$$x=-\frac{5y-2}{9y+5}$$

$$y\neq -\frac{5}{9}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{5}{9} since division by zero is not defined. Multiply both sides of the equation by 9x+5.

$$y\left(9x+5\right)=-5x+2$$

Use the distributive property to multiply y by 9x+5.

$$9yx+5y=-5x+2$$

Add 5x to both sides.

$$9yx+5y+5x=2$$

Subtract 5y from both sides.

$$9yx+5x=2-5y$$

Combine all terms containing x.

$$\left(9y+5\right)x=2-5y$$

Divide both sides by 9y+5.

$$\frac{\left(9y+5\right)x}{9y+5}=\frac{2-5y}{9y+5}$$

Dividing by 9y+5 undoes the multiplication by 9y+5.

$$x=\frac{2-5y}{9y+5}$$

Variable x cannot be equal to -\frac{5}{9}.

$$x=\frac{2-5y}{9y+5}\text{, }x\neq -\frac{5}{9}$$

Solve for y

$$y=-\frac{5x-2}{9x+5}$$

$$x\neq -\frac{5}{9}$$