Solve x=2y-5/7-y

$$x= \frac{ 2y-5 }{ 7-y }$$

Solve for y

$$y=\frac{7x+5}{x+2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Variable y cannot be equal to 7 since division by zero is not defined. Multiply both sides of the equation by -y+7.

$$x\left(-y+7\right)=2y-5$$

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

$$-xy+7x=2y-5$$

Subtract 2y from both sides.

$$-xy+7x-2y=-5$$

Subtract 7x from both sides.

$$-xy-2y=-5-7x$$

Combine all terms containing y.

$$\left(-x-2\right)y=-5-7x$$

The equation is in standard form.

$$\left(-x-2\right)y=-7x-5$$

Divide both sides by -x-2.

$$\frac{\left(-x-2\right)y}{-x-2}=\frac{-7x-5}{-x-2}$$

Dividing by -x-2 undoes the multiplication by -x-2.

$$y=\frac{-7x-5}{-x-2}$$

Divide -5-7x by -x-2.

$$y=\frac{7x+5}{x+2}$$

Variable y cannot be equal to 7.

$$y=\frac{7x+5}{x+2}\text{, }y\neq 7$$

Solve for x

$$x=-\frac{5-2y}{7-y}$$

$$y\neq 7$$