Solve {l}{x+y=3}{y+2=x}{x+z=5}

$$\left\{ \begin{array} { l } { x + y = 3 } \\ { y + 2 = x } \\ { x + z = 5 } \end{array} \right.$$

Solve for x, y, z

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

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

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

Short Steps Using Substitution

Reorder the equations.

$$y+2=x x+y=3 x+z=5$$

Solve y+2=x for x.

$$x=y+2$$

Substitute y+2 for x in the second and third equation.

$$y+2+y=3 y+2+z=5$$

Solve these equations for y and z respectively.

$$y=\frac{1}{2} z=-y+3$$

Substitute \frac{1}{2} for y in the equation z=-y+3.

$$z=-\frac{1}{2}+3$$

Calculate z from z=-\frac{1}{2}+3.

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

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

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

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

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

The system is now solved.

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