Solve y-e^2=(4e-4)(x-e)

$$y- { e }^{ 2 } =(4e-4)(x-e)$$

Solve for x

$$x=-\frac{y+3e^{2}-4e}{4\left(1-e\right)}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4e-4 by x-e.

$$y-e^{2}=4ex-4e^{2}-4x+4e$$

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

$$4ex-4e^{2}-4x+4e=y-e^{2}$$

Add 4e^{2} to both sides.

$$4ex-4x+4e=y-e^{2}+4e^{2}$$

Subtract 4e from both sides.

$$4ex-4x=y-e^{2}+4e^{2}-4e$$

Combine -e^{2} and 4e^{2} to get 3e^{2}.

$$4ex-4x=y+3e^{2}-4e$$

Combine all terms containing x.

$$\left(4e-4\right)x=y+3e^{2}-4e$$

Divide both sides by 4e-4.

$$\frac{\left(4e-4\right)x}{4e-4}=\frac{y+3e^{2}-4e}{4e-4}$$

Dividing by 4e-4 undoes the multiplication by 4e-4.

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

Divide y+3e^{2}-4e by 4e-4.

$$x=\frac{y+3e^{2}-4e}{4\left(e-1\right)}$$

Solve for y

$$y=4\left(e-1\right)\left(x-e\right)+e^{2}$$