Solve {l}{2x-9z=18}{5x-2y+4z=-1}{4z=-16}

$$\left. \begin{array}{l}{ 2 x - 9 z = 18 }\\{ 5 x - 2 y + 4 z = - 1 }\\{ 4 z = - 16 }\end{array} \right.$$

Solve for x, z, y

$$x=-9$$

$$y=-30$$

$$z=-4$$

Solution Steps

Consider the third equation. Divide both sides by 4.

$$z=\frac{-16}{4}$$

Divide -16 by 4 to get -4.

$$z=-4$$

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

$$2x-9\left(-4\right)=18$$

Multiply -9 and -4 to get 36.

$$2x+36=18$$

Subtract 36 from both sides.

$$2x=18-36$$

Subtract 36 from 18 to get -18.

$$2x=-18$$

Divide both sides by 2.

$$x=\frac{-18}{2}$$

Divide -18 by 2 to get -9.

$$x=-9$$

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

$$5\left(-9\right)-2y+4\left(-4\right)=-1$$

Do the multiplications.

$$-45-2y-16=-1$$

Subtract 16 from -45 to get -61.

$$-61-2y=-1$$

Add 61 to both sides.

$$-2y=-1+61$$

Add -1 and 61 to get 60.

$$-2y=60$$

Divide both sides by -2.

$$y=\frac{60}{-2}$$

Divide 60 by -2 to get -30.

$$y=-30$$

The system is now solved.

$$x=-9 z=-4 y=-30$$