Solve {l}{2x+5y-4z=-10}{-2y-z=1}{z=3}

$$\left\{ \begin{array}{l}{ 2 x + 5 y - 4 z = - 10 }\\{ - 2 y - z = 1 }\\{ z = 3 }\end{array} \right.$$

Solve for x, y, z

$$x=6$$

$$y=-2$$

$$z=3$$

Solution Steps

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

$$-2y-3=1$$

Add 3 to both sides.

$$-2y=1+3$$

Add 1 and 3 to get 4.

$$-2y=4$$

Divide both sides by -2.

$$y=\frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$y=-2$$

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

$$2x+5\left(-2\right)-4\times 3=-10$$

Do the multiplications.

$$2x-10-12=-10$$

Subtract 12 from -10 to get -22.

$$2x-22=-10$$

Add 22 to both sides.

$$2x=-10+22$$

Add -10 and 22 to get 12.

$$2x=12$$

Divide both sides by 2.

$$x=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x=6$$

The system is now solved.

$$x=6 y=-2 z=3$$