Solve {l}{1/6x+2/3=1/4x}{text{Solvefor}ytext{where}}{y=-1/3}

$$\left. \begin{array} { l } { \frac{1}{6} x + \frac{2}{3} = \frac{1}{4} x }\\ { \text{Solve for } y \text{ where} } \\ { y = -\frac{1}{3} } \end{array} \right.$$

Solve for x, y

$$y=-\frac{1}{3}\approx -0.333333333$$

Solution Steps

Consider the first equation. Subtract \frac{1}{4}x from both sides.

$$\frac{1}{6}x+\frac{2}{3}-\frac{1}{4}x=0$$

Combine \frac{1}{6}x and -\frac{1}{4}x to get -\frac{1}{12}x.

$$-\frac{1}{12}x+\frac{2}{3}=0$$

Subtract \frac{2}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{12}x=-\frac{2}{3}$$

Multiply both sides by -12, the reciprocal of -\frac{1}{12}.

$$x=-\frac{2}{3}\left(-12\right)$$

Multiply -\frac{2}{3} and -12 to get 8.

$$x=8$$

The system is now solved.

$$x=8 y=-\frac{1}{3}$$