Solve {l}{y=2x-5}{z=6y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = 2 x - 5 }\\ { z = 6 y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a+30}{12}$$

$$y=\frac{a}{6}$$

$$z=a$$

Short Steps Using Substitution

Substitute 2x-5 for y in the equation z=6y.

$$z=6\left(2x-5\right)$$

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

$$x=\frac{5}{2}+\frac{1}{12}z z=a$$

Substitute a for z in the equation x=\frac{5}{2}+\frac{1}{12}z.

$$x=\frac{5}{2}+\frac{1}{12}a$$

Substitute \frac{5}{2}+\frac{1}{12}a for x in the equation y=2x-5.

$$y=2\left(\frac{5}{2}+\frac{1}{12}a\right)-5$$

Calculate y from y=2\left(\frac{5}{2}+\frac{1}{12}a\right)-5.

$$y=\frac{1}{6}a$$

The system is now solved.

$$x=\frac{5}{2}+\frac{1}{12}a y=\frac{1}{6}a z=a$$