Solve {l}{x+y+z=3}{y+2z=1.5}{250x+284(y+z)=281}

$$\left. \begin{array} { l } { x + y + z = 3 } \\ { y + 2 z = 1.5 } \\ { 250 x + 284 ( y + z ) = 281 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{571}{34} = 16\frac{27}{34} \approx 16.794117647$$

$$y = -\frac{989}{34} = -29\frac{3}{34} \approx -29.088235294$$

$$z = \frac{260}{17} = 15\frac{5}{17} \approx 15.294117647$$

Short Steps Using Substitution

Solve x+y+z=3 for x.

$$x=-y-z+3$$

Substitute -y-z+3 for x in the equation 250x+284\left(y+z\right)=281.

$$250\left(-y-z+3\right)+284\left(y+z\right)=281$$

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

$$y=-2z+1.5 z=-y-\frac{469}{34}$$

Substitute -2z+1.5 for y in the equation z=-y-\frac{469}{34}.

$$z=-\left(-2z+1.5\right)-\frac{469}{34}$$

Solve z=-\left(-2z+1.5\right)-\frac{469}{34} for z.

$$z=\frac{260}{17}$$

Substitute \frac{260}{17} for z in the equation y=-2z+1.5.

$$y=-2\times \frac{260}{17}+1.5$$

Calculate y from y=-2\times \frac{260}{17}+1.5.

$$y=-\frac{989}{34}$$

Substitute -\frac{989}{34} for y and \frac{260}{17} for z in the equation x=-y-z+3.

$$x=-\left(-\frac{989}{34}\right)-\frac{260}{17}+3$$

Calculate x from x=-\left(-\frac{989}{34}\right)-\frac{260}{17}+3.

$$x=\frac{571}{34}$$

The system is now solved.

$$x=\frac{571}{34} y=-\frac{989}{34} z=\frac{260}{17}$$