Solve {l}{x+y+z=3}{2x+3y+28=7}{4x+6y+4z=4}

$$\left. \begin{array} { l } { x + y + z = 3 } \\ { 2 x + 3 y + 28 = 7 } \\ { 4 x + 6 y + 4 z = 4 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

$$y=-4$$

$$z = \frac{23}{2} = 11\frac{1}{2} = 11.5$$

Short Steps Using Substitution

Solve x+y+z=3 for x.

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

Substitute -y-z+3 for x in the second and third equation.

$$2\left(-y-z+3\right)+3y+28=7 4\left(-y-z+3\right)+6y+4z=4$$

Solve these equations for z and y respectively.

$$z=\frac{27}{2}+\frac{1}{2}y y=-4$$

Substitute -4 for y in the equation z=\frac{27}{2}+\frac{1}{2}y.

$$z=\frac{27}{2}+\frac{1}{2}\left(-4\right)$$

Calculate z from z=\frac{27}{2}+\frac{1}{2}\left(-4\right).

$$z=\frac{23}{2}$$

Substitute \frac{23}{2} for z and -4 for y in the equation x=-y-z+3.

$$x=-\left(-4\right)-\frac{23}{2}+3$$

Calculate x from x=-\left(-4\right)-\frac{23}{2}+3.

$$x=-\frac{9}{2}$$

The system is now solved.

$$x=-\frac{9}{2} y=-4 z=\frac{23}{2}$$