Solve {l}{p=-4}{q=-2}{r={(|p|-q)}{(q+6)}}{s=30}{t=31}{u=r}{v=s}{w=t}{text{Solvefor}x,y,ztext{where}}{x=u}{y=v}{z=w}

$$\left. \begin{array} { l } { p = -4 }\\ { q = -2 }\\ { r = {(| p | - q)} {(q + 6)} }\\ { s = 30 }\\ { t = 31 }\\ { u = r }\\ { v = s }\\ { w = t }\\ { \text{Solve for } x,y,z \text{ where} } \\ { x = u }\\ { y = v }\\ { z = w } \end{array} \right.$$

Solve for p, q, r, s, t, u, v, w, x, y, z

$$x=24$$

$$y=30$$

$$z=31$$

Solution Steps

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

$$r=\left(|-4|-\left(-2\right)\right)\left(-2+6\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$r=\left(4-\left(-2\right)\right)\left(-2+6\right)$$

Multiply -1 and -2 to get 2.

$$r=\left(4+2\right)\left(-2+6\right)$$

Add 4 and 2 to get 6.

$$r=6\left(-2+6\right)$$

Add -2 and 6 to get 4.

$$r=6\times 4$$

Multiply 6 and 4 to get 24.

$$r=24$$

Consider the equation (6). Insert the known values of variables into the equation.

$$u=24$$

Consider the equation (9). Insert the known values of variables into the equation.

$$x=24$$

The system is now solved.

$$p=-4 q=-2 r=24 s=30 t=31 u=24 v=30 w=31 x=24 y=30 z=31$$