Solve {l}{7z-3=2(x_{x}-3y)}{+3z-7=4x}{4div5z=3(2x-y)}

$$\left. \begin{array}{l}{ 7 z - 3 = 2 ( x _ { x } - 3 y ) }\\{ + 3 z - 7 = 4 x }\\{ 4 \div 5 z = 3 ( 2 x - y ) }\end{array} \right.$$

Solve for x, y, z

$$x=\frac{5x_{x}}{48}-\frac{1}{2}$$

$$y=\frac{37x_{x}}{216}-\frac{13}{9}$$

$$z=\frac{5x_{x}}{36}+\frac{5}{3}$$

Short Steps Using Substitution

Solve 7z-3=2\left(x_{x}-3y\right) for y.

$$y=\frac{1}{3}x_{x}-\frac{7}{6}z+\frac{1}{2}$$

Substitute \frac{1}{3}x_{x}-\frac{7}{6}z+\frac{1}{2} for y in the equation \frac{4}{5}z=3\left(2x-y\right).

$$\frac{4}{5}z=3\left(2x-\left(\frac{1}{3}x_{x}-\frac{7}{6}z+\frac{1}{2}\right)\right)$$

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

$$x=\frac{3}{4}z-\frac{7}{4} z=\frac{5}{9}-\frac{20}{9}x+\frac{10}{27}x_{x}$$

Substitute \frac{3}{4}z-\frac{7}{4} for x in the equation z=\frac{5}{9}-\frac{20}{9}x+\frac{10}{27}x_{x}.

$$z=\frac{5}{9}-\frac{20}{9}\left(\frac{3}{4}z-\frac{7}{4}\right)+\frac{10}{27}x_{x}$$

Solve z=\frac{5}{9}-\frac{20}{9}\left(\frac{3}{4}z-\frac{7}{4}\right)+\frac{10}{27}x_{x} for z.

$$z=\frac{5}{3}+\frac{5}{36}x_{x}$$

Substitute \frac{5}{3}+\frac{5}{36}x_{x} for z in the equation x=\frac{3}{4}z-\frac{7}{4}.

$$x=\frac{3}{4}\left(\frac{5}{3}+\frac{5}{36}x_{x}\right)-\frac{7}{4}$$

Calculate x from x=\frac{3}{4}\left(\frac{5}{3}+\frac{5}{36}x_{x}\right)-\frac{7}{4}.

$$x=-\frac{1}{2}+\frac{5}{48}x_{x}$$

Substitute \frac{5}{3}+\frac{5}{36}x_{x} for z in the equation y=\frac{1}{3}x_{x}-\frac{7}{6}z+\frac{1}{2}.

$$y=\frac{1}{3}x_{x}-\frac{7}{6}\left(\frac{5}{3}+\frac{5}{36}x_{x}\right)+\frac{1}{2}$$

Calculate y from y=\frac{1}{3}x_{x}-\frac{7}{6}\left(\frac{5}{3}+\frac{5}{36}x_{x}\right)+\frac{1}{2}.

$$y=-\frac{13}{9}+\frac{37}{216}x_{x}$$

The system is now solved.

$$x=-\frac{1}{2}+\frac{5}{48}x_{x} y=-\frac{13}{9}+\frac{37}{216}x_{x} z=\frac{5}{3}+\frac{5}{36}x_{x}$$