Solve {l}{{(6)}=x+5/2-3x-2/12}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { {(6)} = \frac{x + 5}{2} - \frac{3 x - 2}{12} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{40}{3} = 13\frac{1}{3} \approx 13.333333333$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 2,12.

$$72=6\left(x+5\right)-\left(3x-2\right)$$

Use the distributive property to multiply 6 by x+5.

$$72=6x+30-\left(3x-2\right)$$

To find the opposite of 3x-2, find the opposite of each term.

$$72=6x+30-3x+2$$

Combine 6x and -3x to get 3x.

$$72=3x+30+2$$

Add 30 and 2 to get 32.

$$72=3x+32$$

Swap sides so that all variable terms are on the left hand side.

$$3x+32=72$$

Subtract 32 from both sides.

$$3x=72-32$$

Subtract 32 from 72 to get 40.

$$3x=40$$

Divide both sides by 3.

$$x=\frac{40}{3}$$

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

$$y=\frac{40}{3}$$

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

$$z=\frac{40}{3}$$

The system is now solved.

$$x=\frac{40}{3} y=\frac{40}{3} z=\frac{40}{3}$$