Solve {l}{x+y=14}{y+z=15}{x+z=16}

$$\left\{ \begin{array} { l } { x + y = 14 } \\ { y + z = 15 } \\ { x + z = 16 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

$$y = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

$$z = \frac{17}{2} = 8\frac{1}{2} = 8.5$$

Short Steps Using Substitution

Solve x+y=14 for x.

$$x=-y+14$$

Substitute -y+14 for x in the equation x+z=16.

$$-y+14+z=16$$

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

$$y=-z+15 z=y+2$$

Substitute -z+15 for y in the equation z=y+2.

$$z=-z+15+2$$

Solve z=-z+15+2 for z.

$$z=\frac{17}{2}$$

Substitute \frac{17}{2} for z in the equation y=-z+15.

$$y=-\frac{17}{2}+15$$

Calculate y from y=-\frac{17}{2}+15.

$$y=\frac{13}{2}$$

Substitute \frac{13}{2} for y in the equation x=-y+14.

$$x=-\frac{13}{2}+14$$

Calculate x from x=-\frac{13}{2}+14.

$$x=\frac{15}{2}$$

The system is now solved.

$$x=\frac{15}{2} y=\frac{13}{2} z=\frac{17}{2}$$