Solve {c}{x-z=-4}{4y-z=9}{2x+5y=13}

$$\left. \begin{array} { c } { x - z = - 4 } \\ { 4 y - z = 9 } \\ { 2 x + 5 y = 13 } \end{array} \right.$$

Solve for x, z, y

$$x=-1$$

$$y=3$$

$$z=3$$

Short Steps Using Substitution

Solve x-z=-4 for x.

$$x=z-4$$

Substitute z-4 for x in the equation 2x+5y=13.

$$2\left(z-4\right)+5y=13$$

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

$$z=4y-9 y=-\frac{2}{5}z+\frac{21}{5}$$

Substitute 4y-9 for z in the equation y=-\frac{2}{5}z+\frac{21}{5}.

$$y=-\frac{2}{5}\left(4y-9\right)+\frac{21}{5}$$

Solve y=-\frac{2}{5}\left(4y-9\right)+\frac{21}{5} for y.

$$y=3$$

Substitute 3 for y in the equation z=4y-9.

$$z=4\times 3-9$$

Calculate z from z=4\times 3-9.

$$z=3$$

Substitute 3 for z in the equation x=z-4.

$$x=3-4$$

Calculate x from x=3-4.

$$x=-1$$

The system is now solved.

$$x=-1 z=3 y=3$$