Solve {l}{2/3x+1=7/3}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{2}{3} x + 1 = \frac{7}{3} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Subtract 1 from both sides.

$$\frac{2}{3}x=\frac{7}{3}-1$$

Subtract 1 from \frac{7}{3} to get \frac{4}{3}.

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

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x=\frac{4}{3}\times \frac{3}{2}$$

Multiply \frac{4}{3} and \frac{3}{2} to get 2.

$$x=2$$

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

$$y=2$$

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

$$z=2$$

The system is now solved.

$$x=2 y=2 z=2$$