Solve y=x+4/-x+3

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

Solve for x

$$x=\frac{3y-4}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

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

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

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

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

Add yx to both sides.

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

Subtract 4 from both sides.

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

Combine all terms containing x.

$$\left(1+y\right)x=3y-4$$

The equation is in standard form.

$$\left(y+1\right)x=3y-4$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{3y-4}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=\frac{3y-4}{y+1}$$

Variable x cannot be equal to 3.

$$x=\frac{3y-4}{y+1}\text{, }x\neq 3$$

Solve for y

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

$$x\neq 3$$