Solve {r}{3x+2y+z=1}{y-z=2}{2z=4}

$$\left. \begin{array} { r } { 3 x + 2 y + z = 1 } \\ { y - z = 2 } \\ { 2 z = 4 } \end{array} \right.$$

Solve for x, y, z

$$x=-3$$

$$y=4$$

$$z=2$$

Solution Steps

Consider the third equation. Divide both sides by 2.

$$z=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$z=2$$

Consider the second equation. Insert the known values of variables into the equation.

$$y-2=2$$

Add 2 to both sides.

$$y=2+2$$

Add 2 and 2 to get 4.

$$y=4$$

Consider the first equation. Insert the known values of variables into the equation.

$$3x+2\times 4+2=1$$

Multiply 2 and 4 to get 8.

$$3x+8+2=1$$

Add 8 and 2 to get 10.

$$3x+10=1$$

Subtract 10 from both sides.

$$3x=1-10$$

Subtract 10 from 1 to get -9.

$$3x=-9$$

Divide both sides by 3.

$$x=\frac{-9}{3}$$

Divide -9 by 3 to get -3.

$$x=-3$$

The system is now solved.

$$x=-3 y=4 z=2$$