Solve {l}{1-x/x-2=1/2}{text{Solvefor}ytext{where}}{y=-2}

$$\left. \begin{array} { l } { \frac{1 - x}{x - 2} = \frac{1}{2} }\\ { \text{Solve for } y \text{ where} } \\ { y = -2 } \end{array} \right.$$

Solve for x, y

$$y=-2$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right), the least common multiple of x-2,2.

$$2\left(1-x\right)=x-2$$

Use the distributive property to multiply 2 by 1-x.

$$2-2x=x-2$$

Subtract x from both sides.

$$2-2x-x=-2$$

Combine -2x and -x to get -3x.

$$2-3x=-2$$

Subtract 2 from both sides.

$$-3x=-2-2$$

Subtract 2 from -2 to get -4.

$$-3x=-4$$

Divide both sides by -3.

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

Fraction \frac{-4}{-3} can be simplified to \frac{4}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{3}$$

The system is now solved.

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