Solve y=2/4-x+3

$$y= \frac{ 2 }{ 4-x } +3$$

Solve for x

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

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by -x+4.

$$y\left(-x+4\right)=2+\left(-x+4\right)\times 3$$

Use the distributive property to multiply y by -x+4.

$$-yx+4y=2+\left(-x+4\right)\times 3$$

Use the distributive property to multiply -x+4 by 3.

$$-yx+4y=2-3x+12$$

Add 2 and 12 to get 14.

$$-yx+4y=14-3x$$

Add 3x to both sides.

$$-yx+4y+3x=14$$

Subtract 4y from both sides.

$$-yx+3x=14-4y$$

Combine all terms containing x.

$$\left(-y+3\right)x=14-4y$$

The equation is in standard form.

$$\left(3-y\right)x=14-4y$$

Divide both sides by -y+3.

$$\frac{\left(3-y\right)x}{3-y}=\frac{14-4y}{3-y}$$

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

$$x=\frac{14-4y}{3-y}$$

Divide -4y+14 by -y+3.

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

Variable x cannot be equal to 4.

$$x=\frac{2\left(7-2y\right)}{3-y}\text{, }x\neq 4$$

Solve for y

$$y=-\frac{3x-14}{4-x}$$

$$x\neq 4$$