Question

X+y=1/9
Y+z=2/9
Z+x=5/9

Answer 1

Answer on Question #72717 - Subject - Differential Equations

**Given:** $x + y = \frac{1}{9}, y + z = \frac{2}{9}, z + x = \frac{5}{9}$.

**To Find:** Find the solution.

**Solution:** To find the solution of the system, we will try to eliminate one variable using two equations. After getting new equation, solve the new equation with the remaining equation.

$$x + y = \frac{1}{9} \quad \text{(1)}$$ $$y + z = \frac{2}{9} \quad \text{(2)}$$ $$z + x = \frac{5}{9} \quad \text{(3)}$$

First solve equation (1) and (2) to eliminate 'y'

$$x + y = \frac{1}{9}$$ $$y + z = \frac{2}{9}$$

On subtraction, we get

$$x - z = \frac{-1}{9} \quad \text{(4)}$$

Now, solve equation 4 with equation 1,

On addition, we get

$$z + x = \frac{5}{9}$$ $$x - z = \frac{-1}{9}$$ $$\Rightarrow 2x = \frac{4}{9}$$ $$\Rightarrow x = \frac{2}{9}$$

Put the value of $x$ in equation 1 and 3, we get

$$\begin{array}{l} \frac{2}{9} + y = \frac{1}{9} \quad \Rightarrow y = \frac{1}{9} - \frac{2}{9} \\ \Rightarrow y = \frac{-1}{9} \\ \end{array}$$

And $z + \frac{2}{9} = \frac{5}{9}$

$$\Rightarrow z = \frac{5}{9} - \frac{2}{9}$$ $$\Rightarrow z = \frac{3}{9} = \frac{1}{3}$$

Hence, the solution of the system is $x = \frac{2}{9}, y = \frac{-1}{9}, z = \frac{1}{3}$ .

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