Solve {c}{xy=8000}{(n+40)(y-10)=8000}

$$\left. \begin{array} { c } { x y = 8000 } \\ { ( n + 40 ) ( y - 10 ) = 8000 } \end{array} \right.$$

Solve for x, y

$$x=\frac{800\left(n+40\right)}{n+840}$$

$$y=\frac{10\left(n+840\right)}{n+40}$$

$$n\neq -840\text{ and }n\neq -40$$

Steps Using Substitution

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$\left(n+40\right)\left(y-10\right)=8000$$

Multiply 40+n times y-10.

$$\left(n+40\right)y-10n-400=8000$$

Subtract -400-10n from both sides of the equation.

$$\left(n+40\right)y=10n+8400$$

Divide both sides by 40+n.

$$y=\frac{10\left(n+840\right)}{n+40}$$

Substitute \frac{10\left(840+n\right)}{40+n} for y in yx=8000. Because the resulting equation contains only one variable, you can solve for x directly.

$$\frac{10\left(n+840\right)}{n+40}x=8000$$

Divide 8000 by \frac{10\left(840+n\right)}{40+n}.

$$x=\frac{800\left(n+40\right)}{n+840}$$

The system is now solved.

$$y=\frac{10\left(n+840\right)}{n+40},x=\frac{800\left(n+40\right)}{n+840}$$