Solve {l}{7/9x-4/9x=1/4+5/12}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{7}{9} x - \frac{4}{9} x = \frac{1}{4} + \frac{5}{12} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Combine \frac{7}{9}x and -\frac{4}{9}x to get \frac{1}{3}x.

$$\frac{1}{3}x=\frac{1}{4}+\frac{5}{12}$$

Add \frac{1}{4} and \frac{5}{12} to get \frac{2}{3}.

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

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

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

Multiply \frac{2}{3} and 3 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.

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