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

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

Solve for p, q, r, s, t, u, v, w

$$u=24$$

$$v=30$$

$$w=31$$

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.

$$u=24$$

The system is now solved.

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