Solve {c}{z=-x-2y-10}{-3y=27}{-10x-2y-2=10}

$$\left. \begin{array} { c } { z = - x - 2 y - 10 } \\ { - 3 y = 27 } \\ { - 10 x - 2 y - 2 = 10 } \end{array} \right.$$

Solve for z, x, y

$$x=\frac{3}{5}=0.6$$

$$y=-9$$

$$z = \frac{37}{5} = 7\frac{2}{5} = 7.4$$

Solution Steps

Consider the second equation. Divide both sides by -3.

$$y=\frac{27}{-3}$$

Divide 27 by -3 to get -9.

$$y=-9$$

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

$$-10x-2\left(-9\right)-2=10$$

Multiply -2 and -9 to get 18.

$$-10x+18-2=10$$

Subtract 2 from 18 to get 16.

$$-10x+16=10$$

Subtract 16 from both sides.

$$-10x=10-16$$

Subtract 16 from 10 to get -6.

$$-10x=-6$$

Divide both sides by -10.

$$x=\frac{-6}{-10}$$

Reduce the fraction \frac{-6}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{3}{5}$$

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

$$z=-\frac{3}{5}-2\left(-9\right)-10$$

Multiply -2 and -9 to get 18.

$$z=-\frac{3}{5}+18-10$$

Add -\frac{3}{5} and 18 to get \frac{87}{5}.

$$z=\frac{87}{5}-10$$

Subtract 10 from \frac{87}{5} to get \frac{37}{5}.

$$z=\frac{37}{5}$$

The system is now solved.

$$z=\frac{37}{5} x=\frac{3}{5} y=-9$$