Solve {l}{9+47z=6}{x-4+2z=5}{x-y-3z=-10}

$$\left. \begin{array} { l } { 9 + 47 z = 6 } \\ { x - 4 + 2 z = 5 } \\ { x - y - 3 z = - 10 } \end{array} \right.$$

Solve for z, x, y

$$x = \frac{429}{47} = 9\frac{6}{47} \approx 9.127659574$$

$$y = \frac{908}{47} = 19\frac{15}{47} \approx 19.319148936$$

$$z=-\frac{3}{47}\approx -0.063829787$$

Solution Steps

Consider the first equation. Subtract 9 from both sides.

$$47z=6-9$$

Subtract 9 from 6 to get -3.

$$47z=-3$$

Divide both sides by 47.

$$z=-\frac{3}{47}$$

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

$$x-4+2\left(-\frac{3}{47}\right)=5$$

Multiply 2 and -\frac{3}{47} to get -\frac{6}{47}.

$$x-4-\frac{6}{47}=5$$

Subtract \frac{6}{47} from -4 to get -\frac{194}{47}.

$$x-\frac{194}{47}=5$$

Add \frac{194}{47} to both sides.

$$x=5+\frac{194}{47}$$

Add 5 and \frac{194}{47} to get \frac{429}{47}.

$$x=\frac{429}{47}$$

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

$$\frac{429}{47}-y-3\left(-\frac{3}{47}\right)=-10$$

Multiply -3 and -\frac{3}{47} to get \frac{9}{47}.

$$\frac{429}{47}-y+\frac{9}{47}=-10$$

Add \frac{429}{47} and \frac{9}{47} to get \frac{438}{47}.

$$\frac{438}{47}-y=-10$$

Subtract \frac{438}{47} from both sides.

$$-y=-10-\frac{438}{47}$$

Subtract \frac{438}{47} from -10 to get -\frac{908}{47}.

$$-y=-\frac{908}{47}$$

Divide both sides by -1.

$$y=\frac{-\frac{908}{47}}{-1}$$

Express \frac{-\frac{908}{47}}{-1} as a single fraction.

$$y=\frac{-908}{47\left(-1\right)}$$

Multiply 47 and -1 to get -47.

$$y=\frac{-908}{-47}$$

Fraction \frac{-908}{-47} can be simplified to \frac{908}{47} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{908}{47}$$

The system is now solved.

$$z=-\frac{3}{47} x=\frac{429}{47} y=\frac{908}{47}$$