Zitsanzo za Mafunso Okhudza Machitidwe Osalingana Olunjika
Dongosolo la kusalingana kolunjika ndi nthambi ya masamu yomwe imakhudza ubale pakati pa kusalingana kolunjika. Dongosololi lili ndi kusalingana kuwiri kapena kuposerapo komwe kumafunika kuthetsa mavuto kuti mupeze yankho lomwe limakwaniritsa kusalingana konse nthawi imodzi. Makambirano a machitidwe a kusalingana kolunjika nthawi zambiri amapezeka mu maphunziro a masamu pamlingo wa sekondale ndi sekondale, m'mafunso a mayeso komanso machitidwe a tsiku ndi tsiku.
Machitidwe osalingana a mzere ali ndi ntchito zambiri zenizeni, kuyambira kukonza zinthu ndi kukonzekera ndalama mpaka kukonza zinthu. Kumvetsetsa mfundo izi sikuti ndikofunikira kokha pothetsa mavuto a masamu kusukulu komanso kumakonzekeretsa ophunzira kuthetsa mavuto a tsiku ndi tsiku mwanzeru komanso moyenera. Pansipa pali zitsanzo za mavuto ndi zokambirana zokhudza machitidwe osalingana a mzere.
Chitsanzo cha Funso 1
Funso:
Dziwani njira yothetsera mavuto ya dongosolo lotsatirali la kusalingana kolunjika:
\[
\kuyamba{milandu}
x + y \leq 6 \\
x – y \geq 2
\mapeto{milandu}
\]
Kukambirana:
1. Jambulani malire a kusalingana kulikonse:
Pa \(x + y \leq 6\), tijambula mzere \(x + y = 6\):
– Pamene \(x = 0\), \(y = 6\) ipanga mfundo (0, 6).
– Pamene \(y = 0\), \(x = 6\) ipanga mfundo (6, 0).
Pa \(x – y \geq 2\), tijambula mzere \(x – y = 2\):
– Pamene \(x = 2\), \(y = 0\) ipanga mfundo (2, 0).
– Pamene \(y = -2\), \(x = 0\) ipanga mfundo (0, -2).
2. Dziwani malo okhala:
– Mzere \(x + y = 6\) umaugawa m'magawo awiri, ndipo timayang'ana mfundo imodzi yoyesera yomwe siili pamzere, mwachitsanzo mfundo (0, 0):
\[
0 + 0 \leq 6 \quad (\text{true})
\]
Kotero, dera lomwe likukwaniritsa lili pansi kapena kumanzere kwa mzere \(x + y = 6\).
– Mzere \(x – y = 2\) umagawanso chinsalucho m'magawo awiri, ndipo timayang'ana mfundo (0, 0):
\[
0 – 0 \geq 2 \quad (\text{false})
\]
Kotero, dera lomwe likukwaniritsa liri pamwamba kapena kumanja kwa mzere \(x – y = 2\).
3. Dziwani malo omwe madera awiriwa akulumikizana:
Yankho la dongosololi ndi dera lomwe limakwaniritsa kusalingana konseku. Timafunafuna malo olumikizirana a madera awiriwa omwe akugwirizana ndi komwe kusalingana kulikonse kukupita.
Pomaliza:
Seti ya mayankho a dongosolo la kusalingana kolunjika ndi mfundo zonse zomwe zili pamzere wa zigawo ziwiri zomwe zimakwaniritsa zofunikira \(x + y \leq 6\) ndi \(x - y \geq 2\).
Chitsanzo cha Funso 2
Funso:
Dziwani njira yothetsera mavuto ya dongosolo lotsatirali la kusalingana kolunjika mu gawo loyamba:
\[
\kuyamba{milandu}
2x + 3y \leq 12 \\
x \geq 0 \\
y \geq 0 \\
\mapeto{milandu}
\]
Kukambirana:
1. Jambulani malire a kusalingana kulikonse:
Pa \(2x + 3y \leq 12\), tijambula mzere \(2x + 3y = 12\):
– Pamene \(x = 0\), \(y = 4\) ipanga mfundo (0, 4).
– Pamene \(y = 0\), \(x = 6\) ipanga mfundo (6, 0).
2. Dziwani malo okhala:
– Mzere \(2x + 3y = 12\) ndi malo oyesera (0, 0):
\[
2(0) + 3(0) \leq 12 \quad (\text{true})
\]
Kotero, dera lomwe likukwaniritsa lili pansi kapena kumanzere kwa mzere \(2x + 3y = 12\).
– \(x \geq 0\) ndi \(y \geq 0\) zikusonyeza kuti mfundo yothetsera ili mu gawo loyamba.
3. Dziwani malo omwe madera awiriwa akulumikizana:
Yankho la dongosololi ndi dera lomwe lili mu gawo loyamba lomwe lili pansi kapena kumanzere kwa mzere \(2x + 3y = 12\).
Pomaliza:
Seti ya mayankho a dongosolo la kusalingana kolunjika ndi mfundo zomwe zili mu gawo loyamba la quadrant zomwe zimakwaniritsa \(2x + 3y \leq 12\).
Chitsanzo cha Funso 3
Funso:
Dziwani njira yothetsera mavuto ya dongosolo lotsatirali la kusalingana kolunjika:
\[
\kuyamba{milandu}
y \geq 2x – 3 \\
y \leq -x + 1
\mapeto{milandu}
\]
Kukambirana:
1. Jambulani malire a kusalingana kulikonse:
Pa \(y \geq 2x - 3\), tijambula mzere \(y = 2x - 3\):
– Pamene \(x = 0\), \(y = -3\) ipanga mfundo (0, -3).
– Pamene \(y = 0\), \(x = 1,5\) ipanga mfundo (1.5, 0).
Pa \(y \leq -x + 1\), timajambula mzere \(y = -x + 1\):
– Pamene \(x = 0\), \(y = 1\) ipanga mfundo (0, 1).
– Pamene \(y = 0\), \(x = 1\) ipanga mfundo (1, 0).
2. Dziwani malo okhala:
– Mzere \(y \geq 2x – 3\) wayesedwa ndi mfundo (0, 0):
\[
0 \geq 2(0) – 3 \quad (\text{true})
\]
Kotero, dera lomwe likukwaniritsa liri pamwamba kapena kumanja kwa mzere \(2x - 3\).
– Mzere \(y \leq -x + 1\) wayesedwa ndi mfundo (0, 0):
\[
0 \leq -0 + 1 \quad (\text{true})
\]
Kotero, dera lomwe likukwaniritsa liri pansi kapena kumanzere kwa mzere \(-x + 1\).
3. Dziwani malo omwe madera awiriwa akulumikizana:
Yankho la dongosololi ndi dera lomwe limakwaniritsa kusalingana konseku. Tikuyang'ana dera lomwe pali kusagwirizana pakati pa kusalingana kuwiriku.
Pomaliza:
Seti ya mayankho a dongosolo la kusalingana kolunjika ndi mfundo zomwe zili pampata wa chigawo zomwe zimakwaniritsa \(y \geq 2x - 3\) ndi \(y \leq -x + 1\).
Mwa kumvetsetsa momwe mungathetsere machitidwe a kusalingana kolunjika, tikuyembekeza kuti ophunzira adzakhala ndi luso lotha kuthetsa mavuto a masamu ndikugwiritsa ntchito mfundozi pazochitika za tsiku ndi tsiku. Tikukhulupirira kuti, zitsanzo za mavuto ndi zokambiranazi zithandiza ophunzira kuphunzira ndikumvetsetsa mfundo zoyambira za machitidwe a kusalingana kolunjika.
