Solve {l}{5y+z=0}{x+2y=0}{x=-2}

$$\left\{ \begin{array} { l } { 5 y + z = 0 } \\ { x + 2 y = 0 } \\ { x = - 2 } \end{array} \right.$$

Solve for y, z, x

$$x=-2$$

$$y=1$$

$$z=-5$$

Solution Steps

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

$$-2+2y=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$2y=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$y=1$$

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

$$5\times 1+z=0$$

Multiply 5 and 1 to get 5.

$$5+z=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$z=-5$$

The system is now solved.

$$y=1 z=-5 x=-2$$