Solve {l}{x+y=5}{y+z=3}{x+z=7}

$$\left. \begin{array} { l } { x + y = 5 } \\ { y + z = 3 } \\ { x + z = 7 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$y=\frac{1}{2}=0.5$$

$$z = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Short Steps Using Substitution

Solve x+y=5 for x.

$$x=-y+5$$

Substitute -y+5 for x in the equation x+z=7.

$$-y+5+z=7$$

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

$$y=-z+3 z=y+2$$

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

$$z=-z+3+2$$

Solve z=-z+3+2 for z.

$$z=\frac{5}{2}$$

Substitute \frac{5}{2} for z in the equation y=-z+3.

$$y=-\frac{5}{2}+3$$

Calculate y from y=-\frac{5}{2}+3.

$$y=\frac{1}{2}$$

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

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

Calculate x from x=-\frac{1}{2}+5.

$$x=\frac{9}{2}$$

The system is now solved.

$$x=\frac{9}{2} y=\frac{1}{2} z=\frac{5}{2}$$