Solve Matrix

$$\left( \begin{array} { r r } { 4 } & { 3 } \\ { - 2 } & { x } \end{array} \right) - \left( \begin{array} { l l } { y } & { 4 } \\ { z } & { 2 } \end{array} \right) = \left( \begin{array} { l l } { 2 } & { w } \\ { 5 } & { - 1 } \end{array} \right)$$

Solve for y, w, z, x

$$x=1$$

$$y=2$$

$$z=-7$$

$$w=-1$$

Solution Steps

Consider the first equation. Subtract 4 from both sides.

$$-y=2-4$$

Subtract 4 from 2 to get -2.

$$-y=-2$$

Divide both sides by -1.

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

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$y=2$$

Consider the second equation. Swap sides so that all variable terms are on the left hand side.

$$w=-1$$

Consider the third equation. Add 2 to both sides.

$$-z=5+2$$

Add 5 and 2 to get 7.

$$-z=7$$

Divide both sides by -1.

$$z=-7$$

Consider the fourth equation. Add 2 to both sides.

$$x=-1+2$$

Add -1 and 2 to get 1.

$$x=1$$

The system is now solved.

$$y=2 w=-1 z=-7 x=1$$