Solve {l}{x+y=26/15}{z=x-y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { x + y = \frac{26}{15} }\\ { z = x - y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a}{2}+\frac{13}{15}$$

$$y=-\frac{a}{2}+\frac{13}{15}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=x-y x+y=\frac{26}{15} a=z$$

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

$$a=x-y$$

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

$$y=-x+\frac{26}{15} x=a+y$$

Substitute -x+\frac{26}{15} for y in the equation x=a+y.

$$x=a-x+\frac{26}{15}$$

Solve x=a-x+\frac{26}{15} for x.

$$x=\frac{13}{15}+\frac{1}{2}a$$

Substitute \frac{13}{15}+\frac{1}{2}a for x in the equation y=-x+\frac{26}{15}.

$$y=-\left(\frac{13}{15}+\frac{1}{2}a\right)+\frac{26}{15}$$

Calculate y from y=-\left(\frac{13}{15}+\frac{1}{2}a\right)+\frac{26}{15}.

$$y=\frac{13}{15}-\frac{1}{2}a$$

Substitute \frac{13}{15}-\frac{1}{2}a for y and \frac{13}{15}+\frac{1}{2}a for x in the equation z=x-y.

$$z=\frac{13}{15}+\frac{1}{2}a-\left(\frac{13}{15}-\frac{1}{2}a\right)$$

Calculate z from z=\frac{13}{15}+\frac{1}{2}a-\left(\frac{13}{15}-\frac{1}{2}a\right).

$$z=a$$

The system is now solved.

$$x=\frac{13}{15}+\frac{1}{2}a y=\frac{13}{15}-\frac{1}{2}a z=a$$