Solve {l}{z=-2}{-3y+4z=4}{-x+2y-3z=-7}

$$\left\{ \begin{array}{l}{ z = - 2 }\\{ - 3 y + 4 z = 4 }\\{ - x + 2 y - 3 z = - 7 }\end{array} \right.$$

Solve for z, y, x

$$x=5$$

$$y=-4$$

$$z=-2$$

Solution Steps

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

$$-3y+4\left(-2\right)=4$$

Multiply 4 and -2 to get -8.

$$-3y-8=4$$

Add 8 to both sides.

$$-3y=4+8$$

Add 4 and 8 to get 12.

$$-3y=12$$

Divide both sides by -3.

$$y=\frac{12}{-3}$$

Divide 12 by -3 to get -4.

$$y=-4$$

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

$$-x+2\left(-4\right)-3\left(-2\right)=-7$$

Do the multiplications.

$$-x-8+6=-7$$

Add -8 and 6 to get -2.

$$-x-2=-7$$

Add 2 to both sides.

$$-x=-7+2$$

Add -7 and 2 to get -5.

$$-x=-5$$

Divide both sides by -1.

$$x=\frac{-5}{-1}$$

Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.

$$x=5$$

The system is now solved.

$$z=-2 y=-4 x=5$$