Solve {l}{x+Y+z=1}{Y+2z=1.5}{256x+284(Y+z)=281.2}

$$\left. \begin{array} { l } { x + Y + z = 1 } \\ { Y + 2 z = 1.5 } \\ { 256 x + 284 ( Y + z ) = 281.2 } \end{array} \right.$$

Solve for x, Y, z

$$x=0.1$$

$$z=0.6$$

$$Y=0.3$$

Short Steps Using Substitution

Solve x+Y+z=1 for x.

$$x=-Y-z+1$$

Substitute -Y-z+1 for x in the equation 256x+284\left(Y+z\right)=281.2.

$$256\left(-Y-z+1\right)+284\left(Y+z\right)=281.2$$

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

$$Y=-2z+1.5 z=\frac{9}{10}-Y$$

Substitute -2z+1.5 for Y in the equation z=\frac{9}{10}-Y.

$$z=\frac{9}{10}-\left(-2z+1.5\right)$$

Solve z=\frac{9}{10}-\left(-2z+1.5\right) for z.

$$z=\frac{3}{5}$$

Substitute \frac{3}{5} for z in the equation Y=-2z+1.5.

$$Y=-2\times \frac{3}{5}+1.5$$

Calculate Y from Y=-2\times \frac{3}{5}+1.5.

$$Y=\frac{3}{10}$$

Substitute \frac{3}{10} for Y and \frac{3}{5} for z in the equation x=-Y-z+1.

$$x=-\frac{3}{10}-\frac{3}{5}+1$$

Calculate x from x=-\frac{3}{10}-\frac{3}{5}+1.

$$x=\frac{1}{10}$$

The system is now solved.

$$x=\frac{1}{10} Y=\frac{3}{10} z=\frac{3}{5}$$