Solve {l}{x=2}{y=3}{z=2|1-x|-5|-y|}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { x = 2 }\\ { y = 3 }\\ { z = 2 | 1 - x | -5 | - y | }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a=-13$$

Solution Steps

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

$$z=2|1-2|-5|-3|$$

Subtract 2 from 1 to get -1.

$$z=2|-1|-5|-3|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -1 is 1.

$$z=2\times 1-5|-3|$$

Multiply 2 and 1 to get 2.

$$z=2-5|-3|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$z=2-5\times 3$$

Multiply 5 and 3 to get 15.

$$z=2-15$$

Subtract 15 from 2 to get -13.

$$z=-13$$

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

$$a=-13$$

The system is now solved.

$$x=2 y=3 z=-13 a=-13$$