Solve {l}{12x+17-6x-5=18x+24+6x+12}{y=5z}{text{Solvefor}atext{where}}{a=y}

$$\left. \begin{array} { l } { 12 x + 17 - 6 x - 5 = 18 x + 24 + 6 x + 12 }\\ { y = 5 z }\\ { \text{Solve for } a \text{ where} } \\ { a = y } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

$$y=a$$

$$z=\frac{a}{5}$$

Short Steps Using Substitution

Reorder the equations.

$$y=5z 12x+17-6x-5=18x+24+6x+12 a=y$$

Substitute 5z for y in the equation a=y.

$$a=5z$$

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

$$x=-\frac{4}{3} z=\frac{1}{5}a$$

Substitute \frac{1}{5}a for z in the equation y=5z.

$$y=5\times \frac{1}{5}a$$

Calculate y from y=5\times \frac{1}{5}a.

$$y=a$$

The system is now solved.

$$x=-\frac{4}{3} y=a z=\frac{1}{5}a$$