Solve Matrix

$$\left. \begin{array} { l l } { x + y + z = 6 } \\ { 2 x + 11 y = 24 } \\ { y = 12 } \end{array} \right.$$

Solve for x, y, z

$$x=-54$$

$$y=12$$

$$z=48$$

Solution Steps

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

$$2x+11\times 12=24$$

Multiply 11 and 12 to get 132.

$$2x+132=24$$

Subtract 132 from both sides.

$$2x=24-132$$

Subtract 132 from 24 to get -108.

$$2x=-108$$

Divide both sides by 2.

$$x=\frac{-108}{2}$$

Divide -108 by 2 to get -54.

$$x=-54$$

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

$$-54+12+z=6$$

Add -54 and 12 to get -42.

$$-42+z=6$$

Add 42 to both sides.

$$z=6+42$$

Add 6 and 42 to get 48.

$$z=48$$

The system is now solved.

$$x=-54 y=12 z=48$$