Solve {l}{4x+8y+2z+6w=2}{-y-6z-2w=-8}{-2z-2w=-4}{-3w=-9}

$$\left. \begin{array}{l}{ 4 x + 8 y + 2 z + 6 w = 2 }\\{ - y - 6 z - 2 w = - 8 }\\{ - 2 z - 2 w = - 4 }\\{ - 3 w = - 9 }\end{array} \right.$$

Solve for x, y, z, w

$$x = -\frac{39}{2} = -19\frac{1}{2} = -19.5$$

$$y=8$$

$$z=-1$$

$$w=3$$

Solution Steps

Consider the fourth equation. Divide both sides by -3.

$$w=\frac{-9}{-3}$$

Divide -9 by -3 to get 3.

$$w=3$$

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

$$-2z-2\times 3=-4$$

Multiply -2 and 3 to get -6.

$$-2z-6=-4$$

Add 6 to both sides.

$$-2z=-4+6$$

Add -4 and 6 to get 2.

$$-2z=2$$

Divide both sides by -2.

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

Divide 2 by -2 to get -1.

$$z=-1$$

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

$$-y-6\left(-1\right)-2\times 3=-8$$

Do the multiplications.

$$-y+6-6=-8$$

Subtract 6 from 6 to get 0.

$$-y=-8$$

Divide both sides by -1.

$$y=\frac{-8}{-1}$$

Fraction \frac{-8}{-1} can be simplified to 8 by removing the negative sign from both the numerator and the denominator.

$$y=8$$

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

$$4x+8\times 8+2\left(-1\right)+6\times 3=2$$

Do the multiplications.

$$4x+64-2+18=2$$

Subtract 2 from 64 to get 62.

$$4x+62+18=2$$

Add 62 and 18 to get 80.

$$4x+80=2$$

Subtract 80 from both sides.

$$4x=2-80$$

Subtract 80 from 2 to get -78.

$$4x=-78$$

Divide both sides by 4.

$$x=\frac{-78}{4}$$

Reduce the fraction \frac{-78}{4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{39}{2}$$

The system is now solved.

$$x=-\frac{39}{2} y=8 z=-1 w=3$$