Solve {l}{x/6-2x-3/2=0}{y={(8)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x}{6} - \frac{2 x - 3}{2} = 0 }\\ { y = {(8)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=8$$

Solution Steps

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

$$x-3\left(2x-3\right)=0$$

Use the distributive property to multiply -3 by 2x-3.

$$x-6x+9=0$$

Combine x and -6x to get -5x.

$$-5x+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-5x=-9$$

Divide both sides by -5.

$$x=\frac{-9}{-5}$$

Fraction \frac{-9}{-5} can be simplified to \frac{9}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{5}$$

The system is now solved.

$$x=\frac{9}{5} y=8 z=8$$