Solve {l}{4(-5y-5z-2)-5y+4z=19}{-5y-5z-2+5y-z=-20}

$$\left. \begin{array} { l } { 4 ( - 5 y - 5 z - 2 ) - 5 y + 4 z = 19 } \\ { - 5 y - 5 z - 2 + 5 y - z = - 20 } \end{array} \right.$$

Solve for y, z

$$y=-3$$

$$z=3$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 4 by -5y-5z-2.

$$-20y-20z-8-5y+4z=19$$

Combine -20y and -5y to get -25y.

$$-25y-20z-8+4z=19$$

Combine -20z and 4z to get -16z.

$$-25y-16z-8=19$$

Add 8 to both sides.

$$-25y-16z=19+8$$

Add 19 and 8 to get 27.

$$-25y-16z=27$$

Consider the second equation. Combine -5y and 5y to get 0.

$$-5z-2-z=-20$$

Combine -5z and -z to get -6z.

$$-6z-2=-20$$

Add 2 to both sides.

$$-6z=-20+2$$

Add -20 and 2 to get -18.

$$-6z=-18$$

Divide both sides by -6.

$$z=\frac{-18}{-6}$$

Divide -18 by -6 to get 3.

$$z=3$$

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

$$-25y-16\times 3=27$$

Multiply -16 and 3 to get -48.

$$-25y-48=27$$

Add 48 to both sides.

$$-25y=27+48$$

Add 27 and 48 to get 75.

$$-25y=75$$

Divide both sides by -25.

$$y=\frac{75}{-25}$$

Divide 75 by -25 to get -3.

$$y=-3$$

The system is now solved.

$$y=-3 z=3$$