Solve {l}{200=x}{text{Solvefor}ytext{where}}{y=4/6x+1/2{(2/6x)}}

$$\left. \begin{array} { l } { 200 = x }\\ { \text{Solve for } y \text{ where} } \\ { y = \frac{4}{6} x + \frac{1}{2} {(\frac{2}{6} x)} } \end{array} \right.$$

Solve for x, y

$$y = \frac{500}{3} = 166\frac{2}{3} \approx 166.666666667$$

Solution Steps

Consider the first equation. Swap sides so that all variable terms are on the left hand side.

$$x=200$$

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

$$y=\frac{4}{6}\times 200+\frac{1}{2}\times \frac{2}{6}\times 200$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$y=\frac{2}{3}\times 200+\frac{1}{2}\times \frac{2}{6}\times 200$$

Multiply \frac{2}{3} and 200 to get \frac{400}{3}.

$$y=\frac{400}{3}+\frac{1}{2}\times \frac{2}{6}\times 200$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$y=\frac{400}{3}+\frac{1}{2}\times \frac{1}{3}\times 200$$

Multiply \frac{1}{2} and \frac{1}{3} to get \frac{1}{6}.

$$y=\frac{400}{3}+\frac{1}{6}\times 200$$

Multiply \frac{1}{6} and 200 to get \frac{100}{3}.

$$y=\frac{400}{3}+\frac{100}{3}$$

Add \frac{400}{3} and \frac{100}{3} to get \frac{500}{3}.

$$y=\frac{500}{3}$$

The system is now solved.

$$x=200 y=\frac{500}{3}$$