Solve {l}{7x-9y-2{(x-18y)}=0}{z=3{(x+3y)}-{(x+8y)}}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 7 x - 9 y - 2 {(x - 18 y)} = 0 }\\ { z = 3 {(x + 3 y)} - {(x + 8 y)} }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{27a}{49}$$

$$y=-\frac{5a}{49}$$

$$z=a$$

Short Steps Using Substitution

Reorder the equations.

$$z=3\left(x+3y\right)-\left(x+8y\right) 7x-9y-2\left(x-18y\right)=0 a=z$$

Calculate z from z=3\left(x+3y\right)-\left(x+8y\right).

$$z=2x+y$$

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

$$a=2x+y$$

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

$$y=-\frac{5}{27}x x=\frac{1}{2}a-\frac{1}{2}y$$

Substitute -\frac{5}{27}x for y in the equation x=\frac{1}{2}a-\frac{1}{2}y.

$$x=\frac{1}{2}a-\frac{1}{2}\left(-\frac{5}{27}\right)x$$

Solve x=\frac{1}{2}a-\frac{1}{2}\left(-\frac{5}{27}\right)x for x.

$$x=\frac{27}{49}a$$

Substitute \frac{27}{49}a for x in the equation y=-\frac{5}{27}x.

$$y=-\frac{5}{27}\times \frac{27}{49}a$$

Calculate y from y=-\frac{5}{27}\times \frac{27}{49}a.

$$y=-\frac{5}{49}a$$

Substitute -\frac{5}{49}a for y and \frac{27}{49}a for x in the equation z=2x+y.

$$z=2\times \frac{27}{49}a-\frac{5}{49}a$$

Calculate z from z=2\times \frac{27}{49}a-\frac{5}{49}a.

$$z=a$$

The system is now solved.

$$x=\frac{27}{49}a y=-\frac{5}{49}a z=a$$