Solve {l}{{(frac{1*{(2)}+1}{2})}{(x-2/3)}=0}{y=2}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { {(\frac{1 \cdot {(2)} + 1}{2})} {(x - \frac{2}{3})} = 0 }\\ { y = 2 }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for x, y, z, a, b, c

$$c=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(1\times 2+1\right)\left(x-\frac{2}{3}\right)=0$$

Multiply 1 and 2 to get 2.

$$3\left(2+1\right)\left(x-\frac{2}{3}\right)=0$$

Add 2 and 1 to get 3.

$$3\times 3\left(x-\frac{2}{3}\right)=0$$

Multiply 3 and 3 to get 9.

$$9\left(x-\frac{2}{3}\right)=0$$

Use the distributive property to multiply 9 by x-\frac{2}{3}.

$$9x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$9x=6$$

Divide both sides by 9.

$$x=\frac{6}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

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

The system is now solved.

$$x=\frac{2}{3} y=2 z=2 a=2 b=2 c=2$$