Solve {l}{x+y=1}{y+3z=25}{3x-z=0}

$$\left\{ \begin{array} { l } { x + y = 1 } \\ { y + 3 z = 25 } \\ { 3 x - z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=3$$

$$y=-2$$

$$z=9$$

Short Steps Using Substitution

Solve x+y=1 for x.

$$x=-y+1$$

Substitute -y+1 for x in the equation 3x-z=0.

$$3\left(-y+1\right)-z=0$$

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

$$y=-3z+25 z=-3y+3$$

Substitute -3z+25 for y in the equation z=-3y+3.

$$z=-3\left(-3z+25\right)+3$$

Solve z=-3\left(-3z+25\right)+3 for z.

$$z=9$$

Substitute 9 for z in the equation y=-3z+25.

$$y=-3\times 9+25$$

Calculate y from y=-3\times 9+25.

$$y=-2$$

Substitute -2 for y in the equation x=-y+1.

$$x=-\left(-2\right)+1$$

Calculate x from x=-\left(-2\right)+1.

$$x=3$$

The system is now solved.

$$x=3 y=-2 z=9$$