Cov Lus Nug Piv Txwv Sib Tham Txog Cov Txheej Txheem Tsis Sib Npaug Linear
Ib qho system ntawm linear inequalities yog ib ceg ntawm kev suav lej uas cuam tshuam txog kev sib raug zoo ntawm ntau qhov linear inequalities. Lub system no muaj ob lossis ntau qhov inequalities uas xav tau kev daws teeb meem kom nrhiav tau ib qho kev daws teeb meem uas ua tiav tag nrho cov inequalities tib lub sijhawm. Kev sib tham txog cov systems ntawm linear inequalities feem ntau ntsib hauv cov ntawv kawm lej ntawm cov tsev kawm ntawv theem siab thiab theem siab, ob qho tib si hauv cov lus nug xeem thiab kev xyaum txhua hnub.
Cov txheej txheem kev tsis sib luag ntawm kab ncaj muaj ntau yam kev siv hauv lub neej tiag tiag, xws li kev siv cov peev txheej zoo tshaj plaws thiab kev npaj nyiaj txiag mus rau kev thauj mus los. Kev nkag siab txog cov ntsiab lus no tsis yog tsuas yog qhov tseem ceeb rau kev daws teeb meem lej hauv tsev kawm ntawv xwb tab sis kuj npaj cov tub ntxhais kawm kom daws cov teeb meem txhua hnub kom zoo thiab ua tau zoo. Hauv qab no yog qee qhov piv txwv ntawm cov teeb meem thiab kev sib tham txog cov txheej txheem kev tsis sib luag ntawm kab ncaj.
Piv txwv lus nug 1
Lo lus nug:
Txheeb xyuas cov txheej txheem daws teeb meem ntawm cov kab ke linear inequalities hauv qab no:
\[
\begin{cov ntaub ntawv}
x + y \geq 6 \\
x – y \geq 2
\end{cases}
\]
Kev Sib Tham:
1. Kos ib txoj kab ciam teb rau txhua qhov tsis sib npaug:
Rau \(x + y \leq 6\), peb kos kab \(x + y = 6\):
– Thaum \(x = 0\), \(y = 6\) tsim tau qhov taw tes (0, 6).
– Thaum \(y = 0\), \(x = 6\) tsim tau qhov taw tes (6, 0).
Rau \(x – y \geq 2\), peb kos kab \(x – y = 2\):
– Thaum \(x = 2\), \(y = 0\) tsim tau qhov taw tes (2, 0).
– Thaum \(y = -2\), \(x = 0\) tsim cov taw tes (0, -2).
2. Txheeb xyuas thaj chaw nyob:
- Kab \(x + y = 6\) faib nws ua ob thaj tsam, thiab peb xyuas ib qho chaw sim uas tsis nyob ntawm kab, piv txwv li qhov chaw (0, 0):
\[
0 + 0 \leq 6 \quad (\text{true})
\]
Yog li, thaj chaw uas txaus siab yog hauv qab lossis sab laug ntawm kab \(x + y = 6\).
- Kab \(x – y = 2\) faib qhov screen dua ua ob thaj tsam, thiab peb xyuas qhov point (0, 0):
\[
0 – 0 \geq 2 \quad (\text{false})
\]
Yog li, thaj chaw uas txaus siab yog nyob rau saum toj lossis sab xis ntawm kab \(x - y = 2\).
3. Txheeb xyuas qhov kev sib tshuam ntawm ob thaj tsam:
Qhov kev daws teeb meem rau lub kaw lus yog thaj chaw uas txaus siab rau ob qho kev tsis sib luag. Peb nrhiav qhov kev sib tshuam ntawm ob thaj chaw uas sib raug rau qhov kev taw qhia ntawm txhua qhov kev tsis sib luag.
Kesimpulan:
Cov txheej txheem daws teeb meem ntawm ib qho system ntawm linear inequalities yog txhua lub ntsiab lus hauv qhov kev sib tshuam ntawm ob thaj tsam uas ua tiav cov xwm txheej \(x + y \leq 6\) thiab \(x – y \geq 2\).
Piv txwv lus nug 2
Lo lus nug:
Txheeb xyuas cov txheej txheem daws teeb meem ntawm cov kab ke hauv qab no ntawm cov kab sib npaug linear hauv thawj quadrant:
\[
\begin{cov ntaub ntawv}
2x + 3y \geq 12 \\
x \geq 0 \\
y \geq 0 \\
\end{cases}
\]
Kev Sib Tham:
1. Kos ib txoj kab ciam teb rau txhua qhov tsis sib npaug:
Rau \(2x + 3y \leq 12\), peb kos kab \(2x + 3y = 12\):
– Thaum \(x = 0\), \(y = 4\) tsim tau qhov taw tes (0, 4).
– Thaum \(y = 0\), \(x = 6\) tsim tau qhov taw tes (6, 0).
2. Txheeb xyuas thaj chaw nyob:
– Kab \(2x + 3y = 12\) thiab qhov chaw sim (0, 0):
\[
2(0) + 3(0) \leq 12 \quad (\text{true})
\]
Yog li, thaj chaw uas txaus siab yog hauv qab lossis sab laug ntawm kab \(2x + 3y = 12\).
- \(x \geq 0\) thiab \(y \geq 0\) qhia tias qhov chaw daws teeb meem nyob hauv thawj quadrant.
3. Txheeb xyuas qhov kev sib tshuam ntawm ob thaj tsam:
Qhov kev daws teeb meem rau lub system yog thaj chaw hauv thawj quadrant uas nyob hauv qab lossis sab laug ntawm kab \(2x + 3y = 12\).
Kesimpulan:
Cov txheej txheem daws teeb meem ntawm ib qho system ntawm linear inequalities yog cov ntsiab lus nyob rau hauv thawj quadrant uas txaus siab \(2x + 3y \leq 12\).
Piv txwv lus nug 3
Lo lus nug:
Txheeb xyuas cov txheej txheem daws teeb meem ntawm cov kab ke linear inequalities hauv qab no:
\[
\begin{cov ntaub ntawv}
y \geq 2x – 3 \\
y \leq -x + 1
\end{cases}
\]
Kev Sib Tham:
1. Kos ib txoj kab ciam teb rau txhua qhov tsis sib npaug:
Rau \(y \geq 2x – 3\), peb kos kab \(y = 2x – 3\):
– Thaum \(x = 0\), \(y = -3\) tsim tau qhov taw tes (0, -3).
– Thaum \(y = 0\), \(x = 1,5\) tsim tau qhov taw tes (1.5, 0).
Rau \(y \leq -x + 1\), peb kos kab \(y = -x + 1\):
– Thaum \(x = 0\), \(y = 1\) tsim tau qhov taw tes (0, 1).
– Thaum \(y = 0\), \(x = 1\) tsim tau qhov taw tes (1, 0).
2. Txheeb xyuas thaj chaw nyob:
- Kab \(y \geq 2x – 3\) raug sim nrog lub ntsiab lus (0, 0):
\[
0 \geq 2(0) – 3 \quad (\text{true})
\]
Yog li, thaj chaw uas txaus siab yog nyob rau sab saud lossis sab xis ntawm kab \(2x - 3\).
– Kab \(y \leq -x + 1\) raug sim nrog lub ntsiab lus (0, 0):
\[
0 \leq -0 + 1 \quad (\text{true})
\]
Yog li, thaj chaw uas txaus siab yog hauv qab lossis sab laug ntawm kab \(-x + 1\).
3. Txheeb xyuas qhov kev sib tshuam ntawm ob thaj tsam:
Qhov kev daws teeb meem rau lub kaw lus yog thaj chaw uas txaus siab rau ob qho kev tsis sib npaug. Peb tab tom nrhiav thaj chaw ntawm kev sib tshuam ntawm ob qho kev tsis sib npaug.
Kesimpulan:
Cov txheej txheem daws teeb meem ntawm ib qho system ntawm linear inequalities yog cov ntsiab lus nyob rau hauv qhov kev sib tshuam ntawm thaj tsam uas txaus siab \(y \geq 2x - 3\) thiab \(y \leq -x + 1\).
Los ntawm kev nkag siab txog yuav ua li cas daws cov kab ke ntawm cov kab sib npaug, vam tias cov tub ntxhais kawm yuav muaj kev txawj ntse ntau dua hauv kev daws cov teeb meem lej thiab siv cov tswv yim no rau hauv cov xwm txheej txhua hnub. Vam tias, cov piv txwv teeb meem thiab kev sib tham no yuav pab cov tub ntxhais kawm kawm thiab nkag siab txog cov ntsiab lus yooj yim ntawm cov kab ke ntawm cov kab sib npaug.
