Solve {l}{y=-{(frac{1*{(3)}+2}{3})}x+5}{z=x+5}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = -{(\frac{1 \cdot {(3)} + 2}{3})} x + 5 }\\ { z = x + 5 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=a-5$$

$$y=\frac{40-5a}{3}$$

$$z=a$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$3y=15-5x z=x+5 a=z$$

Reorder the equations.

$$z=x+5 3y=15-5x a=z$$

Substitute x+5 for z in the equation a=z.

$$a=x+5$$

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

$$y=5-\frac{5}{3}x x=a-5$$

Substitute a-5 for x in the equation y=5-\frac{5}{3}x.

$$y=5-\frac{5}{3}\left(a-5\right)$$

Calculate y from y=5-\frac{5}{3}\left(a-5\right).

$$y=\frac{40}{3}-\frac{5}{3}a$$

Substitute a-5 for x in the equation z=x+5.

$$z=a-5+5$$

Calculate z from z=a-5+5.

$$z=a$$

The system is now solved.

$$x=a-5 y=\frac{40}{3}-\frac{5}{3}a z=a$$