Solve {l}{x+y=-1}{6y=24}{4x+2y-4z=-36}

$$\left\{ \begin{array}{l}{ x + y = - 1 }\\{ 6 y = 24 }\\{ 4 x + 2 y - 4 z = - 36 }\end{array} \right.$$

Solve for x, y, z

$$x=-5$$

$$y=4$$

$$z=6$$

Solution Steps

Consider the second equation. Divide both sides by 6.

$$y=\frac{24}{6}$$

Divide 24 by 6 to get 4.

$$y=4$$

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

$$x+4=-1$$

Subtract 4 from both sides.

$$x=-1-4$$

Subtract 4 from -1 to get -5.

$$x=-5$$

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

$$4\left(-5\right)+2\times 4-4z=-36$$

Do the multiplications.

$$-20+8-4z=-36$$

Add -20 and 8 to get -12.

$$-12-4z=-36$$

Add 12 to both sides.

$$-4z=-36+12$$

Add -36 and 12 to get -24.

$$-4z=-24$$

Divide both sides by -4.

$$z=\frac{-24}{-4}$$

Divide -24 by -4 to get 6.

$$z=6$$

The system is now solved.

$$x=-5 y=4 z=6$$