Issolvi varepsilon=pi/E(sigma_{1}-v(sigma_{2}+sigma_{3}))

$$\varepsilon = \frac { \pi } { E } ( \sigma _ { 1 } - v ( \sigma _ { 2 } + \sigma _ { 3 } ) )$$

Solvi għal E

$$\left\{\begin{matrix}E=\frac{\pi \left(\sigma _{1}-v\sigma _{3}-v\sigma _{2}\right)}{\epsilon }\text{, }&\sigma _{1}\neq v\left(\sigma _{2}+\sigma _{3}\right)\text{ and }\epsilon \neq 0\text{ and }\sigma _{1}\neq v\sigma _{2}+v\sigma _{3}\\E\neq 0\text{, }&\epsilon =0\text{ and }\sigma _{1}=v\left(\sigma _{2}+\sigma _{3}\right)\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli E ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'E.

$$\epsilon E=\pi \left(\sigma _{1}-v\left(\sigma _{2}+\sigma _{3}\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika v b'\sigma _{2}+\sigma _{3}.

$$\epsilon E=\pi \left(\sigma _{1}-\left(v\sigma _{2}+v\sigma _{3}\right)\right)$$

Biex issib l-oppost ta' v\sigma _{2}+v\sigma _{3}, sib l-oppost ta' kull terminu.

$$\epsilon E=\pi \left(\sigma _{1}-v\sigma _{2}-v\sigma _{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \pi b'\sigma _{1}-v\sigma _{2}-v\sigma _{3}.

$$\epsilon E=\pi \sigma _{1}-\pi v\sigma _{2}-\pi v\sigma _{3}$$

L-ekwazzjoni hija f'forma standard.

$$\epsilon E=\pi \sigma _{1}-\pi v\sigma _{3}-\pi v\sigma _{2}$$

Iddividi ż-żewġ naħat b'\epsilon .

$$\frac{\epsilon E}{\epsilon }=\frac{\pi \left(\sigma _{1}-v\sigma _{3}-v\sigma _{2}\right)}{\epsilon }$$

Meta tiddividi b'\epsilon titneħħa l-multiplikazzjoni b'\epsilon .

$$E=\frac{\pi \left(\sigma _{1}-v\sigma _{3}-v\sigma _{2}\right)}{\epsilon }$$

Il-varjabbi E ma jistax ikun ugwali għal 0.

$$E=\frac{\pi \left(\sigma _{1}-v\sigma _{3}-v\sigma _{2}\right)}{\epsilon }\text{, }E\neq 0$$

Solvi għal v

$$\left\{\begin{matrix}v=\frac{\pi \sigma _{1}-E\epsilon }{\pi \left(\sigma _{2}+\sigma _{3}\right)}\text{, }&E\neq 0\text{ and }\sigma _{2}\neq -\sigma _{3}\\v\in \mathrm{R}\text{, }&\sigma _{1}=\frac{E\epsilon }{\pi }\text{ and }\sigma _{2}=-\sigma _{3}\text{ and }E\neq 0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'E.

$$\epsilon E=\pi \left(\sigma _{1}-v\left(\sigma _{2}+\sigma _{3}\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika v b'\sigma _{2}+\sigma _{3}.

$$\epsilon E=\pi \left(\sigma _{1}-\left(v\sigma _{2}+v\sigma _{3}\right)\right)$$

Biex issib l-oppost ta' v\sigma _{2}+v\sigma _{3}, sib l-oppost ta' kull terminu.

$$\epsilon E=\pi \left(\sigma _{1}-v\sigma _{2}-v\sigma _{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \pi b'\sigma _{1}-v\sigma _{2}-v\sigma _{3}.

$$\epsilon E=\pi \sigma _{1}-\pi v\sigma _{2}-\pi v\sigma _{3}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\pi \sigma _{1}-\pi v\sigma _{2}-\pi v\sigma _{3}=\epsilon E$$

Naqqas \pi \sigma _{1} miż-żewġ naħat.

$$-\pi v\sigma _{2}-\pi v\sigma _{3}=\epsilon E-\pi \sigma _{1}$$

Erġa' ordna t-termini.

$$-\pi v\sigma _{2}-\pi v\sigma _{3}=E\epsilon -\pi \sigma _{1}$$

Ikkombina t-termini kollha li fihom v.

$$\left(-\pi \sigma _{2}-\pi \sigma _{3}\right)v=E\epsilon -\pi \sigma _{1}$$

Iddividi ż-żewġ naħat b'-\pi \sigma _{2}-\pi \sigma _{3}.

$$\frac{\left(-\pi \sigma _{2}-\pi \sigma _{3}\right)v}{-\pi \sigma _{2}-\pi \sigma _{3}}=\frac{E\epsilon -\pi \sigma _{1}}{-\pi \sigma _{2}-\pi \sigma _{3}}$$

Meta tiddividi b'-\pi \sigma _{2}-\pi \sigma _{3} titneħħa l-multiplikazzjoni b'-\pi \sigma _{2}-\pi \sigma _{3}.

$$v=\frac{E\epsilon -\pi \sigma _{1}}{-\pi \sigma _{2}-\pi \sigma _{3}}$$

Iddividi \epsilon E-\pi \sigma _{1} b'-\pi \sigma _{2}-\pi \sigma _{3}.

$$v=\frac{E\epsilon -\pi \sigma _{1}}{-\pi \left(\sigma _{2}+\sigma _{3}\right)}$$