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

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

Solve for x, y, z, a

$$a = \frac{13}{4} = 3\frac{1}{4} = 3.25$$

Solution Steps

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

$$z=3\times \frac{3}{4}+2\times \frac{1}{2}$$

Multiply 3 and \frac{3}{4} to get \frac{9}{4}.

$$z=\frac{9}{4}+2\times \frac{1}{2}$$

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

$$z=\frac{9}{4}+1$$

Add \frac{9}{4} and 1 to get \frac{13}{4}.

$$z=\frac{13}{4}$$

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

$$a=\frac{13}{4}$$

The system is now solved.

$$x=\frac{1}{2} y=\frac{3}{4} z=\frac{13}{4} a=\frac{13}{4}$$