Solve {l}{0=15+5r}{y=-8+(-4r)}{z=-4+(-2r)}

$$\left. \begin{array} { l } { 0 = 15 + 5 r } \\ { y = - 8 + ( - 4 r ) } \\ { z = - 4 + ( - 2 r ) } \end{array} \right.$$

Solve for r, y, z

$$y=4$$

$$z=2$$

$$r=-3$$

Solution Steps

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

$$15+5r=0$$

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$5r=-15$$

Divide both sides by 5.

$$r=\frac{-15}{5}$$

Divide -15 by 5 to get -3.

$$r=-3$$

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

$$y=-8-4\left(-3\right)$$

Multiply -4 and -3 to get 12.

$$y=-8+12$$

Add -8 and 12 to get 4.

$$y=4$$

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

$$z=-4-2\left(-3\right)$$

Multiply -2 and -3 to get 6.

$$z=-4+6$$

Add -4 and 6 to get 2.

$$z=2$$

The system is now solved.

$$r=-3 y=4 z=2$$