Solve {l}{x+4y=325}{x+4z=265}{x+4y+4z=522}

$$\left\{ \begin{array} { l } { x + 4 y = 325 } \\ { x + 4 z = 265 } \\ { x + 4 y + 4 z = 522 } \end{array} \right.$$

Solve for x, y, z

$$x=68$$

$$y = \frac{257}{4} = 64\frac{1}{4} = 64.25$$

$$z = \frac{197}{4} = 49\frac{1}{4} = 49.25$$

Short Steps Using Substitution

Solve x+4y=325 for x.

$$x=-4y+325$$

Substitute -4y+325 for x in the second and third equation.

$$-4y+325+4z=265 -4y+325+4y+4z=522$$

Solve these equations for y and z respectively.

$$y=15+z z=\frac{197}{4}$$

Substitute \frac{197}{4} for z in the equation y=15+z.

$$y=15+\frac{197}{4}$$

Calculate y from y=15+\frac{197}{4}.

$$y=\frac{257}{4}$$

Substitute \frac{257}{4} for y in the equation x=-4y+325.

$$x=-4\times \frac{257}{4}+325$$

Calculate x from x=-4\times \frac{257}{4}+325.

$$x=68$$

The system is now solved.

$$x=68 y=\frac{257}{4} z=\frac{197}{4}$$