Solve {l}{X*y=100}{x+y=100}

$$\left. \begin{array} { l } { X \cdot y = 100 } \\ { x + y = 100 } \end{array} \right.$$

Solve for x, y

$$x=100-\frac{100}{X}$$

$$y=\frac{100}{X}$$

$$X\neq 0$$

Steps Using Substitution

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$Xy=100,y+x=100$$

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.

$$Xy=100$$

Divide both sides by X.

$$y=\frac{100}{X}$$

Substitute \frac{100}{X} for y in the other equation, y+x=100.

$$\frac{100}{X}+x=100$$

Subtract \frac{100}{X} from both sides of the equation.

$$x=100-\frac{100}{X}$$

The system is now solved.

$$y=\frac{100}{X},x=100-\frac{100}{X}$$