Solve {l}{x+a=xy}{a-y=11}{a=4}

$$\left. \begin{array} { l } { x + a = x y } \\ { a - y = 11 } \\ { a = 4 } \end{array} \right.$$

Solve for x, a, y

$$x=-\frac{1}{2}=-0.5$$

$$y=-7$$

$$a=4$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$4-y=11$$

Subtract 4 from both sides.

$$-y=11-4$$

Subtract 4 from 11 to get 7.

$$-y=7$$

Divide both sides by -1.

$$y=-7$$

Consider the first equation. Insert the known values of variables into the equation.

$$x+4=x\left(-7\right)$$

Subtract x\left(-7\right) from both sides.

$$x+4-x\left(-7\right)=0$$

Combine x and -x\left(-7\right) to get 8x.

$$8x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$8x=-4$$

Divide both sides by 8.

$$x=\frac{-4}{8}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{2}$$

The system is now solved.

$$x=-\frac{1}{2} a=4 y=-7$$