Solve {l}{x+y+z=8034}{x*5=y*3}{y*11=2*6}

$$\left. \begin{array} { l } { x + y + z = 8034 } \\ { x \cdot 5 = y \cdot 3 } \\ { y \cdot 11 = 2 \cdot 6 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{36}{55}\approx 0.654545455$$

$$y = \frac{12}{11} = 1\frac{1}{11} \approx 1.090909091$$

$$z = \frac{441774}{55} = 8032\frac{14}{55} \approx 8032.254545455$$

Solution Steps

Consider the third equation. Multiply 2 and 6 to get 12.

$$y\times 11=12$$

Divide both sides by 11.

$$y=\frac{12}{11}$$

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

$$x\times 5=\frac{12}{11}\times 3$$

Multiply \frac{12}{11} and 3 to get \frac{36}{11}.

$$x\times 5=\frac{36}{11}$$

Divide both sides by 5.

$$x=\frac{\frac{36}{11}}{5}$$

Express \frac{\frac{36}{11}}{5} as a single fraction.

$$x=\frac{36}{11\times 5}$$

Multiply 11 and 5 to get 55.

$$x=\frac{36}{55}$$

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

$$\frac{36}{55}+\frac{12}{11}+z=8034$$

Add \frac{36}{55} and \frac{12}{11} to get \frac{96}{55}.

$$\frac{96}{55}+z=8034$$

Subtract \frac{96}{55} from both sides.

$$z=8034-\frac{96}{55}$$

Subtract \frac{96}{55} from 8034 to get \frac{441774}{55}.

$$z=\frac{441774}{55}$$

The system is now solved.

$$x=\frac{36}{55} y=\frac{12}{11} z=\frac{441774}{55}$$