Solve {l}{4x+5z=-18}{-4x+2y=8}{-x=10}

$$\left\{ \begin{array} { l } { 4 x + 5 z = - 18 } \\ { - 4 x + 2 y = 8 } \\ { - x = 10 } \end{array} \right.$$

Solve for x, z, y

$$x=-10$$

$$y=-16$$

$$z = \frac{22}{5} = 4\frac{2}{5} = 4.4$$

Solution Steps

Consider the third equation. Divide both sides by -1.

$$x=-10$$

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

$$4\left(-10\right)+5z=-18$$

Multiply 4 and -10 to get -40.

$$-40+5z=-18$$

Add 40 to both sides.

$$5z=-18+40$$

Add -18 and 40 to get 22.

$$5z=22$$

Divide both sides by 5.

$$z=\frac{22}{5}$$

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

$$-4\left(-10\right)+2y=8$$

Multiply -4 and -10 to get 40.

$$40+2y=8$$

Subtract 40 from both sides.

$$2y=8-40$$

Subtract 40 from 8 to get -32.

$$2y=-32$$

Divide both sides by 2.

$$y=\frac{-32}{2}$$

Divide -32 by 2 to get -16.

$$y=-16$$

The system is now solved.

$$x=-10 z=\frac{22}{5} y=-16$$