Mehlala ea Lipotso tse Buisanang ka Mekhoa ea Litekanyo tse Mola le ho se Lekane
Mekhoa ea li-equation tse otlolohileng le ho se lekane ke sehlooho sa bohlokoa lipalo tse nang le ts'ebeliso e pharaletseng mafapheng a fapaneng, joalo ka moruo, saense le boenjiniere. Sehloohong sena, re tla tšohla mehlala ea mathata a amanang le mekhoa ea li-equation tse otlolohileng le ho se lekane le mokhoa oa ho a rarolla ka botlalo.
Tlhaloso ea Sistimi ea Litekanyo tse Kholo
Sistimi ea li-equation tse otlolohileng e na le li-equation tse peli kapa ho feta tse otlolohileng tse amanang. Mehlala ke ena:
\[
\ qala{maemo}
2x + 3y = 5 \\
4x – y = 1
\qetela{maemo}
\]
Sepheo sa ho rarolla tsamaiso ena ke ho fumana boleng ba \(x\) le \(y\) bo kgotsofatsang diekabone ka bobedi ka nako e le nngwe.
Mekhoa ea ho Rarolla Mekhoa ea Litekanyo tse Kholo
Ho na le mekhoa e 'maloa ea ho rarolla litsamaiso tsa li-equation tse otlolohileng, ho kenyeletsoa:
1. Mokhoa oa ho Nkela Sebaka
2. Mokhoa oa ho Felisa
3. Mokhoa oa Matrix (O fapaneng kapa oa Gauss-Jordan)
Mohlala oa Potso ea 1: Mokhoa oa ho Nkela Sebaka
A re rarolleng tsamaiso e latelang re sebelisa mokhoa oa ho nkela sebaka:
\[
\ qala{maemo}
x + 2y = 10 \\
3x – y = 5
\qetela{maemo}
\]
Langkah-langkah:
1. Arola e 'ngoe ea li-variable ho e 'ngoe ea li-equation.
Ho tloha ho equation ea pele, re arola \(x\):
\[
x = 10 – 2y
\]
2. Kenya polelo e fumanoeng sebakeng sa equation e 'ngoe.
Kenya \(x = 10 – 2y\) sebakeng sa equation ya bobedi:
\[
3(10 – 2y) – y = 5
\]
Rarolla bakeng sa \(y\):
\[
30 – 6y – y = 5
\]
\[
Lilemo tse 30 – 7 = 5
\]
\[
-7y = -25
\]
\[
y = \frac{25}{7}
\]
3. Sebelisa boleng bo fumanoeng ho fumana mefuta e meng.
Kenya sebaka sa \(y = \frac{25}{7}\) hape polelong ya \(x\):
\[
x = 10 – 2\left(\frac{25}{7}\right)
\]
\[
x = 10 – \frac{50}{7}
\]
\[
x = \frac{70}{7} – \frac{50}{7}
\]
\[
x = \frac{20}{7}
\]
Kahoo, ditharollo tsa sistimi ke \( x = \frac{20}{7} \) le \( y = \frac{25}{7} \).
Mohlala oa Potso ea 2: Mokhoa oa ho Felisa
Ka mor'a moo, ha re sebeliseng mokhoa oa ho felisa ho rarolla tsamaiso e latelang:
\[
\ qala{maemo}
2x + 3y = 12 \\
4x + 6y = 24
\qetela{maemo}
\]
Tabeng ena, re bona hore equation ea bobeli ke palo e ngata ea equation ea pele. Ho fokotsa sistimi, re ka atisa equation ea pele ka 2 ebe re e ntša ho equation ea bobeli:
1. Atisa equation ea pele ka 2:
\[
2(2x + 3y) = 2 \cdot 12
\]
\[
4x + 6y = 24
\]
2. Tlosa equation ea pele e atisitsoeng ho equation ea bobeli:
\[
(4x + 6y) – (4x + 6y) = 24 – 24
\]
\[
0 = 0
\]
Sena se fana ka \(0 = 0\), e leng se bontshang hore sistimi e na le ditharollo tse sa feleng mme di-equation tsena di itshetlehile ka tsona.
Mohlala oa Potso ea 3: Ho se lekane ha mola
Ho se lekane ha mola ho latela melao-motheo e tšoanang le ea li-equation tse otlolohileng, empa ho kenyelletsa matšoao a ho se lekane a kang \(<, \leq, >, \geq\). A re shebeng mohlala o bonolo:
\[
\ qala{maemo}
3x – y < 7 \\ 2x + y \geq 4 \end{cases} \] Mehato: 1. Re sebelisa mokhoa oa litšoantšo ho fumana sebaka sa tharollo ea sistimi ena. Kenya kerafo ho se lekane ho hong le ho hong. 2. Fetolela ho se lekane ho equation ho fumana mola oa moeli: Bakeng sa \(3x - y < 7\), mola oa moeli ke \(3x - y = 7\)
