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

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

Solve for x, y, z

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$z=1$$

Short Steps Using Substitution

Solve x+y=2 for x.

$$x=-y+2$$

Substitute -y+2 for x in the second and third equation.

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

Solve these equations for y and z respectively.

$$y=-\frac{5}{2}+z z=-\frac{2}{3}y$$

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

$$z=-\frac{2}{3}\left(-\frac{5}{2}+z\right)$$

Solve z=-\frac{2}{3}\left(-\frac{5}{2}+z\right) for z.

$$z=1$$

Substitute 1 for z in the equation y=-\frac{5}{2}+z.

$$y=-\frac{5}{2}+1$$

Calculate y from y=-\frac{5}{2}+1.

$$y=-\frac{3}{2}$$

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

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

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

$$x=\frac{7}{2}$$

The system is now solved.

$$x=\frac{7}{2} y=-\frac{3}{2} z=1$$