Solve {l}{x=4}{y=-6}{z=|5x-7y|}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { x = 4 }\\ { y = -6 }\\ { z = | 5 x - 7 y | }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a=62$$

Solution Steps

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

$$z=|5\times 4-7\left(-6\right)|$$

Do the multiplications.

$$z=|20+42|$$

Add 20 and 42 to get 62.

$$z=|62|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 62 is 62.

$$z=62$$

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

$$a=62$$

The system is now solved.

$$x=4 y=-6 z=62 a=62$$