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

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

Solve for x, y, z

$$y=-\frac{1}{2}=-0.5$$

$$z = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Solution Steps

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

$$-3\left(2x+1\right)=4$$

Use the distributive property to multiply -3 by 2x+1.

$$-6x-3=4$$

Add 3 to both sides.

$$-6x=4+3$$

Add 4 and 3 to get 7.

$$-6x=7$$

Divide both sides by -6.

$$x=-\frac{7}{6}$$

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

$$y=\frac{3\left(-\frac{7}{6}\right)+2}{3}$$

Multiply 3 and -\frac{7}{6} to get -\frac{7}{2}.

$$y=\frac{-\frac{7}{2}+2}{3}$$

Add -\frac{7}{2} and 2 to get -\frac{3}{2}.

$$y=\frac{-\frac{3}{2}}{3}$$

Express \frac{-\frac{3}{2}}{3} as a single fraction.

$$y=\frac{-3}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$y=\frac{-3}{6}$$

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

$$y=-\frac{1}{2}$$

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

$$z=-3\left(-\frac{7}{6}\right)$$

Multiply -3 and -\frac{7}{6} to get \frac{7}{2}.

$$z=\frac{7}{2}$$

The system is now solved.

$$x=-\frac{7}{6} y=-\frac{1}{2} z=\frac{7}{2}$$