Solve {l}{y=7x+2}{z=3+2y+x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = 7 x + 2 }\\ { z = 3 + 2 y + x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{a-7}{15}$$

$$y=\frac{7a-19}{15}$$

$$z=a$$

Short Steps Using Substitution

Substitute 7x+2 for y in the equation z=3+2y+x.

$$z=3+2\left(7x+2\right)+x$$

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

$$x=-\frac{7}{15}+\frac{1}{15}z z=a$$

Substitute a for z in the equation x=-\frac{7}{15}+\frac{1}{15}z.

$$x=-\frac{7}{15}+\frac{1}{15}a$$

Substitute -\frac{7}{15}+\frac{1}{15}a for x in the equation y=7x+2.

$$y=7\left(-\frac{7}{15}+\frac{1}{15}a\right)+2$$

Calculate y from y=7\left(-\frac{7}{15}+\frac{1}{15}a\right)+2.

$$y=-\frac{19}{15}+\frac{7}{15}a$$

The system is now solved.

$$x=-\frac{7}{15}+\frac{1}{15}a y=-\frac{19}{15}+\frac{7}{15}a z=a$$