Solve {l}{8=2-4x}{y=x}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 8 = 2 - 4 x }\\ { y = x }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Solution Steps

Consider the first equation. Swap sides so that all variable terms are on the left hand side.

$$2-4x=8$$

Subtract 2 from both sides.

$$-4x=8-2$$

Subtract 2 from 8 to get 6.

$$-4x=6$$

Divide both sides by -4.

$$x=\frac{6}{-4}$$

Reduce the fraction \frac{6}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{3}{2}$$

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

$$y=-\frac{3}{2}$$

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

$$z=-\frac{3}{2}$$

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

$$a=-\frac{3}{2}$$

The system is now solved.

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