Solve {l}{3y=11}{z=2x-4y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 3 y = 11 }\\ { z = 2 x - 4 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a}{2}+\frac{22}{3}$$

$$y = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=2x-4y 3y=11 a=z$$

Substitute 2x-4y for z in the equation a=z.

$$a=2x-4y$$

Solve the second equation for y and the third equation for x.

$$y=\frac{11}{3} x=\frac{1}{2}a+2y$$

Substitute \frac{11}{3} for y in the equation x=\frac{1}{2}a+2y.

$$x=\frac{1}{2}a+2\times \frac{11}{3}$$

Calculate x from x=\frac{1}{2}a+2\times \frac{11}{3}.

$$x=\frac{22}{3}+\frac{1}{2}a$$

Substitute \frac{11}{3} for y and \frac{22}{3}+\frac{1}{2}a for x in the equation z=2x-4y.

$$z=2\left(\frac{22}{3}+\frac{1}{2}a\right)-4\times \frac{11}{3}$$

Calculate z from z=2\left(\frac{22}{3}+\frac{1}{2}a\right)-4\times \frac{11}{3}.

$$z=a$$

The system is now solved.

$$x=\frac{22}{3}+\frac{1}{2}a y=\frac{11}{3} z=a$$