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

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

Solve for x, y, z

$$x=5$$

$$y=3$$

$$z=3$$

Solution Steps

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

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

Divide -6 by -2 to get 3.

$$z=3$$

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

$$4y-3\times 3=3$$

Multiply -3 and 3 to get -9.

$$4y-9=3$$

Add 9 to both sides.

$$4y=3+9$$

Add 3 and 9 to get 12.

$$4y=12$$

Divide both sides by 4.

$$y=\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$y=3$$

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

$$-6x+6\times 3+5\times 3=3$$

Do the multiplications.

$$-6x+18+15=3$$

Add 18 and 15 to get 33.

$$-6x+33=3$$

Subtract 33 from both sides.

$$-6x=3-33$$

Subtract 33 from 3 to get -30.

$$-6x=-30$$

Divide both sides by -6.

$$x=\frac{-30}{-6}$$

Divide -30 by -6 to get 5.

$$x=5$$

The system is now solved.

$$x=5 y=3 z=3$$