Solve {l}{3x+y-2x=7}{2x+2y+z=5}{-x+y-z=5}

$$\left\{ \begin{array} { l } { 3 x + y - 2 x = 7 } \\ { 2 x + 2 y + z = 5 } \\ { - x + y - z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

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

$$z=-9$$

Short Steps Using Substitution

Solve 3x+y-2x=7 for y.

$$y=-x+7$$

Substitute -x+7 for y in the second and third equation.

$$2x+2\left(-x+7\right)+z=5 -x-x+7-z=5$$

Solve these equations for z and x respectively.

$$z=-9 x=1-\frac{1}{2}z$$

Substitute -9 for z in the equation x=1-\frac{1}{2}z.

$$x=1-\frac{1}{2}\left(-9\right)$$

Calculate x from x=1-\frac{1}{2}\left(-9\right).

$$x=\frac{11}{2}$$

Substitute \frac{11}{2} for x in the equation y=-x+7.

$$y=-\frac{11}{2}+7$$

Calculate y from y=-\frac{11}{2}+7.

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

The system is now solved.

$$x=\frac{11}{2} y=\frac{3}{2} z=-9$$