Solve y=2-(x-3){(e)^-5}

$$y=2-(x-3) {(e)^{ -5 }}$$

Solve for x

$$x=-e^{5}\left(y-2\right)+3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3 by e^{-5}.

$$y=2-\left(xe^{-5}-3e^{-5}\right)$$

To find the opposite of xe^{-5}-3e^{-5}, find the opposite of each term.

$$y=2-xe^{-5}+3e^{-5}$$

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

$$2-xe^{-5}+3e^{-5}=y$$

Subtract 2 from both sides.

$$-xe^{-5}+3e^{-5}=y-2$$

Subtract 3e^{-5} from both sides.

$$-xe^{-5}=y-2-3e^{-5}$$

The equation is in standard form.

$$\left(-\frac{1}{e^{5}}\right)x=y-\frac{3}{e^{5}}-2$$

Divide both sides by -e^{-5}.

$$\frac{\left(-\frac{1}{e^{5}}\right)x}{-\frac{1}{e^{5}}}=\frac{y-\frac{3}{e^{5}}-2}{-\frac{1}{e^{5}}}$$

Dividing by -e^{-5} undoes the multiplication by -e^{-5}.

$$x=\frac{y-\frac{3}{e^{5}}-2}{-\frac{1}{e^{5}}}$$

Divide y-\frac{3}{e^{5}}-2 by -e^{-5}.

$$x=3+2e^{5}-e^{5}y$$

Solve for y

$$y=-\frac{x-2e^{5}-3}{e^{5}}$$