Rešite frac{14left({a}_{1}+{a}_{1}+13dright)}{2}-frac{11left({a}_{1}+{a}_{1}+b{a}_{2}right)}{2}=19

$$\frac{ 14 \left( { a }_{ 1 } + { a }_{ 1 } +13d \right) }{ 2 } - \frac{ 11 \left( { a }_{ 1 } + { a }_{ 1 } +b { a }_{ 2 } \right) }{ 2 } = 19$$

Rešitev za a_1

$$a_{1}=\frac{11a_{2}b}{6}-\frac{91d}{3}+\frac{19}{3}$$

Koraki za reševanje linearnih enačb

Pomnožite obe strani enačbe s/z 2.

$$14\left(a_{1}+a_{1}+13d\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=38$$

Združite a_{1} in a_{1}, da dobite 2a_{1}.

$$14\left(2a_{1}+13d\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=38$$

Uporabite distributivnost, da pomnožite 14 s/z 2a_{1}+13d.

$$28a_{1}+182d-11\left(a_{1}+a_{1}+ba_{2}\right)=38$$

Združite a_{1} in a_{1}, da dobite 2a_{1}.

$$28a_{1}+182d-11\left(2a_{1}+ba_{2}\right)=38$$

Uporabite distributivnost, da pomnožite -11 s/z 2a_{1}+ba_{2}.

$$28a_{1}+182d-22a_{1}-11ba_{2}=38$$

Združite 28a_{1} in -22a_{1}, da dobite 6a_{1}.

$$6a_{1}+182d-11ba_{2}=38$$

Odštejte 182d na obeh straneh.

$$6a_{1}-11ba_{2}=38-182d$$

Dodajte 11ba_{2} na obe strani.

$$6a_{1}=38-182d+11ba_{2}$$

Enačba je v standardni obliki.

$$6a_{1}=11a_{2}b-182d+38$$

Delite obe strani z vrednostjo 6.

$$\frac{6a_{1}}{6}=\frac{11a_{2}b-182d+38}{6}$$

Z deljenjem s/z 6 razveljavite množenje s/z 6.

$$a_{1}=\frac{11a_{2}b-182d+38}{6}$$

Delite 38-182d+11ba_{2} s/z 6.

$$a_{1}=\frac{11a_{2}b}{6}-\frac{91d}{3}+\frac{19}{3}$$

Rešitev za a_2

$$\left\{\begin{matrix}a_{2}=-\frac{2\left(19-91d-3a_{1}\right)}{11b}\text{, }&b\neq 0\\a_{2}\in \mathrm{R}\text{, }&a_{1}=\frac{19-91d}{3}\text{ and }b=0\end{matrix}\right,$$

Koraki za reševanje linearnih enačb

Pomnožite obe strani enačbe s/z 2.

$$14\left(a_{1}+a_{1}+13d\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=38$$

Združite a_{1} in a_{1}, da dobite 2a_{1}.

$$14\left(2a_{1}+13d\right)-11\left(a_{1}+a_{1}+ba_{2}\right)=38$$

Uporabite distributivnost, da pomnožite 14 s/z 2a_{1}+13d.

$$28a_{1}+182d-11\left(a_{1}+a_{1}+ba_{2}\right)=38$$

Združite a_{1} in a_{1}, da dobite 2a_{1}.

$$28a_{1}+182d-11\left(2a_{1}+ba_{2}\right)=38$$

Uporabite distributivnost, da pomnožite -11 s/z 2a_{1}+ba_{2}.

$$28a_{1}+182d-22a_{1}-11ba_{2}=38$$

Združite 28a_{1} in -22a_{1}, da dobite 6a_{1}.

$$6a_{1}+182d-11ba_{2}=38$$

Odštejte 6a_{1} na obeh straneh.

$$182d-11ba_{2}=38-6a_{1}$$

Odštejte 182d na obeh straneh.

$$-11ba_{2}=38-6a_{1}-182d$$

Enačba je v standardni obliki.

$$\left(-11b\right)a_{2}=38-182d-6a_{1}$$

Delite obe strani z vrednostjo -11b.

$$\frac{\left(-11b\right)a_{2}}{-11b}=\frac{38-182d-6a_{1}}{-11b}$$

Z deljenjem s/z -11b razveljavite množenje s/z -11b.

$$a_{2}=\frac{38-182d-6a_{1}}{-11b}$$

Delite 38-6a_{1}-182d s/z -11b.

$$a_{2}=-\frac{2\left(19-91d-3a_{1}\right)}{11b}$$