Solve {l}{-2x=6}{5x-2y+5z=-9}{4x+3z=-6}

$$\left\{ \begin{array}{l}{ - 2 x = 6 }\\{ 5 x - 2 y + 5 z = - 9 }\\{ 4 x + 3 z = - 6 }\end{array} \right.$$

Solve for x, y, z

$$x=-3$$

$$y=2$$

$$z=2$$

Solution Steps

Consider the first equation. Divide both sides by -2.

$$x=\frac{6}{-2}$$

Divide 6 by -2 to get -3.

$$x=-3$$

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

$$4\left(-3\right)+3z=-6$$

Multiply 4 and -3 to get -12.

$$-12+3z=-6$$

Add 12 to both sides.

$$3z=-6+12$$

Add -6 and 12 to get 6.

$$3z=6$$

Divide both sides by 3.

$$z=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$z=2$$

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

$$5\left(-3\right)-2y+5\times 2=-9$$

Do the multiplications.

$$-15-2y+10=-9$$

Add -15 and 10 to get -5.

$$-5-2y=-9$$

Add 5 to both sides.

$$-2y=-9+5$$

Add -9 and 5 to get -4.

$$-2y=-4$$

Divide both sides by -2.

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

Divide -4 by -2 to get 2.

$$y=2$$

The system is now solved.

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