Solve {l}{x=-1/2}{y=-3/4}{z=-2x-4y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { x = -\frac{1}{2} }\\ { y = -\frac{3}{4} }\\ { z = -2 x - 4 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a=4$$

Solution Steps

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

$$z=-2\left(-\frac{1}{2}\right)-4\left(-\frac{3}{4}\right)$$

Multiply -2 and -\frac{1}{2} to get 1.

$$z=1-4\left(-\frac{3}{4}\right)$$

Multiply -4 and -\frac{3}{4} to get 3.

$$z=1+3$$

Add 1 and 3 to get 4.

$$z=4$$

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

$$a=4$$

The system is now solved.

$$x=-\frac{1}{2} y=-\frac{3}{4} z=4 a=4$$