Solve {l}{{(frac{1*{(3)}+2}{3})}x-4/9={(frac{1*{(6)}+5}{6})}x-0}{y=5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { {(\frac{1 \cdot {(3)} + 2}{3})} x - \frac{4}{9} = {(\frac{1 \cdot {(6)} + 5}{6})} x - 0 }\\ { y = 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=5$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 18, the least common multiple of 3,9,6.

$$6\left(1\times 3+2\right)x-8=3\left(1\times 6+5\right)x-0$$

Multiply 1 and 3 to get 3.

$$6\left(3+2\right)x-8=3\left(1\times 6+5\right)x-0$$

Add 3 and 2 to get 5.

$$6\times 5x-8=3\left(1\times 6+5\right)x-0$$

Multiply 6 and 5 to get 30.

$$30x-8=3\left(1\times 6+5\right)x-0$$

Multiply 1 and 6 to get 6.

$$30x-8=3\left(6+5\right)x-0$$

Add 6 and 5 to get 11.

$$30x-8=3\times 11x-0$$

Multiply 3 and 11 to get 33.

$$30x-8=33x-0$$

Subtract 33x from both sides.

$$30x-8-33x=-0$$

Combine 30x and -33x to get -3x.

$$-3x-8=-0$$

Multiply -1 and 0 to get 0.

$$-3x-8=0$$

Add 8 to both sides. Anything plus zero gives itself.

$$-3x=8$$

Divide both sides by -3.

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

The system is now solved.

$$x=-\frac{8}{3} y=5 z=5$$