Solve {r}{2-5w=-2}{-2z+5w=3}

$$\left. \begin{array} { r } { 2 - 5 w = - 2 } \\ { - 2 z + 5 w = 3 } \end{array} \right.$$

Solve for w, z

$$z=\frac{1}{2}=0.5$$

$$w=\frac{4}{5}=0.8$$

Solution Steps

Consider the first equation. Subtract 2 from both sides.

$$-5w=-2-2$$

Subtract 2 from -2 to get -4.

$$-5w=-4$$

Divide both sides by -5.

$$w=\frac{-4}{-5}$$

Fraction \frac{-4}{-5} can be simplified to \frac{4}{5} by removing the negative sign from both the numerator and the denominator.

$$w=\frac{4}{5}$$

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

$$-2z+5\times \frac{4}{5}=3$$

Multiply 5 and \frac{4}{5} to get 4.

$$-2z+4=3$$

Subtract 4 from both sides.

$$-2z=3-4$$

Subtract 4 from 3 to get -1.

$$-2z=-1$$

Divide both sides by -2.

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

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

$$z=\frac{1}{2}$$

The system is now solved.

$$w=\frac{4}{5} z=\frac{1}{2}$$